This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Consider the products of consecutive integers, (m+9)!/9!, m >= 1. First, 10 is divisible by 2 and 5, but there is a prime gap since 3 is missing from the factorization. 10*11 is divisible by 2, 5, and 11, but 3 and 7 are missing. 10*11*12 is divisible by 2, 3, 5, and 11, but 7 is missing. 10*11*12*13 is divisible by all primes up to 13, except 7. But 10*11*12*13*14 is indeed divisible by every prime from 2 to 13. So a(10) = 5 because 5 consecutive numbers are multiplied together.
Contribution from R. J. Mathar, Feb 27 2010: (Start) A000040v := proc(pmax) L := {} ; for i from 1 do if ithprime(i) <= pmax then L := L union {ithprime(i)} ; else return L; end if end do ; end: A164799 := proc(n) local k,p ; if n = 1 then return 1 ; end if; for k from 1 do p := ifactors(mul(n+i,i=0..k-1))[2] ; p := {seq(op(1,d),d=p)} ; pL := A000040v(max(op(p))) ; if p = pL then return k; end if; end do ; end proc: seq(A164799(n),n=1..90) ; (End)
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