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Considered by many to be one of the most influential mathematicians alive today, Neil Sloane has made major contributions to the fields of sphere packing, combinatorics, and error-correcting codes. He is probably best known for being the creator and curator of the On-Line Encyclopedia of Integer Sequences (OEIS), known simply as “Sloane” by its many users. The repository is over 50 years old and contains over 260,000 sequences.

Neil recently turned 76 but his passion for mathematics remains as strong as ever. Talking about a recent project, he writes: “Back in September I was looking at an old sequence in the OEIS. The sequence starts 1, 12, 123, 1234, 12345, ..., 123456789, 12345678910, 1234567891011, ... The n-th term: just write all the decimal numbers from 1 to n in a row and think of this as a big number. The entry for the sequence had a comment that it is expected that there are infinitely many terms which are primes, but that no prime was known, even though Dana Jaconsen had checked the first 64,000 terms. So I asked various friends and correspondents about this, and people extended the search somewhat. In fact Ernst Mayer has set up a cloud-source project to look for primes in the sequence, and the sequence has now been checked to nearly n = 270,000 without finding a prime. But I am hopeful that a prime will appear before we get to n = 10^6. When a prime is found, as it surely will be, it probably won't be the largest prime known, but it will be close to the record (which is held by the latest Mersenne prime). We may make it into the top ten. It will certainly be the largest known prime which is easy to write down! (Explicitly, I mean. You may know that 2^32582657-1 is prime, but you won't be able to write down the decimal expansion without using a computer).”

Neil has agreed to take some time away from his favorite sequences and answer any questions you may have. As usual, ask as many as you'd like, but please, one question per post.

Considered by many to be one of the most influential mathematicians alive today, Neil Sloane has made major contributions to the fields of sphere packing, combinatorics, and error-correcting codes. He is probably best known for being the creator and curator of the On-Line Encyclopedia of Integer Sequences (OEIS), known simply as “Sloane” by its many users. The repository is over 50 years old and contains over 260,000 sequences.

Neil recently turned 76 but his passion for mathematics remains as strong as ever. Talking about a recent project, he writes: “Back in September I was looking at an old sequence in the OEIS. The sequence starts 1, 12, 123, 1234, 12345, ..., 123456789, 12345678910, 1234567891011, ... The n-th term: just write all the decimal numbers from 1 to n in a row and think of this as a big number. The entry for the sequence had a comment that it is expected that there are infinitely many terms which are primes, but that no prime was known, even though Dana Jaconsen had checked the first 64,000 terms. So I asked various friends and correspondents about this, and people extended the search somewhat. In fact Ernst Mayer has set up a cloud-source project to look for primes in the sequence, and the sequence has now been checked to nearly n = 270,000 without finding a prime. But I am hopeful that a prime will appear before we get to n = 10^6. When a prime is found, as it surely will be, it probably won't be the largest prime known, but it will be close to the record (which is held by the latest Mersenne prime). We may make it into the top ten. It will certainly be the largest known prime which is easy to write down! (Explicitly, I mean. You may know that 2^32582657-1 is prime, but you won't be able to write down the decimal expansion without using a computer).”

Neil has agreed to take some time away from his favorite sequences and answer any questions you may have. As usual, ask as many as you'd like, but please, one question per post.

An anonymous reader writes: 75-year-old Neil Sloane is considered by many to be one of the most influential mathematicians of our time, not because of the theorems he's proved, but because of his creation: The Online Encyclopedia of Integer Sequences (OEIS). Quanta Magazine reports: "This giant repository, which celebrated its 50th anniversary last year, contains more than a quarter of a million different sequences of numbers that arise in different mathematical contexts, such as the prime numbers (2, 3, 5, 7, 11 ) or the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13 ). What's the greatest number of cake slices that can be made with n cuts? Look up sequence A000125 in the OEIS. How many chess positions can be created in n moves? That's sequence A048987. The number of ways to arrange n circles in a plane, with only two crossing at any given point, is A250001. That sequence just joined the collection a few months ago. So far, only its first four terms are known; if you can figure out the fifth, Sloane will want to hear from you."