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

2, 8, 587, 114382, 25678050356, 23136292864687, 48471109094902544777, 103805969587115219182432, 905970719001665604796396056038, 88427967009378444685165002293032443131447, 550006721989970936444120719825244586583663666, 285053798960048163188843790902665241600662702868793966427

Offset

1,1

Links

Table of n, a(n) for n=1..12.

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

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 prime(2)=3, these are {1,1,2,2,0,1,2,1,0,0,1, ...}, with the first prime(2)-1=2 consecutive zeros beginning at n=8. Thus a(2)=8.

Prog

(PARI) a(n) = my(p=prime(n)); (p^p-1)/(p-1) + 1-(p^p-p)/(p-1)^2; \\ Michel Marcus, May 19 2024

Crossrefs

Cf. A000110.

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

Extensions

More terms from Michel Marcus, May 19 2024

Status

approved