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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). 0
2, 8, 587, 114382, 25678050356, 23136292864687, 48471109094902544777, 103805969587115219182432, 905970719001665604796396056038, 88427967009378444685165002293032443131447 (list; graph; refs; listen; history; text; internal format)
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 * A076985 A120802 A120838

Adjacent sequences:  A175920 A175921 A175922 * A175924 A175925 A175926

KEYWORD

nonn

AUTHOR

John W. Layman, Oct 18 2010

STATUS

approved

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Last modified October 17 10:50 EDT 2017. Contains 293469 sequences.