A175923 Index of the first occurrence of p(n)-1 consecutive zeros in the sequence of Bell numbers reduced modulo the n-th prime p(n).

2, 8, 587, 114382, 25678050356, 23136292864687, 48471109094902544777, 103805969587115219182432, 905970719001665604796396056038, 88427967009378444685165002293032443131447

Offset

1,1

References

J. W. Layman, Maximum Strings of Bell Numbers Modulo Primes, J. Combin. Theory, Series A, 40 (1985) 161-168.

Links

Table of n, a(n) for n=1..10.

Formula

a(n)=(p^p - 1)/(p - 1) + 1 - (p^p - p)/(p - 1)^2, where p is the n-th prime.

Example

The Bell numbers, A000110, begin {1,1,2,5,15,52,203,877,4140,21147,115975,...} for n=0,1,2,...; modulo the second prime p(2)=3, these are {1,1,2,2,0,1,2,1,0,0,1, ...}, with the first p(2)-1=2 consecutive zeros beginning at n=8. Thus a(2)=8.

Crossrefs

Sequence in context: A023365 A262826 A013554 * A356202 A076985 A120802

Adjacent sequences: A175920 A175921 A175922 * A175924 A175925 A175926

Keyword

nonn

Author

John W. Layman, Oct 18 2010

Status

approved