

A286635


a(n) is the smallest composite (pseudoprime) p such that Bell(n+p) == Bell(n)+Bell(n+1) (mod p).


0



21361, 8, 4, 134, 6, 4, 57, 6, 34, 65, 14, 9, 14, 6, 4, 21, 12, 4, 26, 8, 26, 779, 102, 99, 33, 8, 4, 14, 12, 4, 9, 6, 70, 33, 169, 25, 98, 8, 4, 14, 410, 4, 458, 6, 10, 25, 6, 26, 14, 8, 4, 122, 6, 4, 231, 8, 836, 62, 18, 74, 39, 8, 4, 1101, 14, 4, 81, 8, 68, 9, 6
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OFFSET

0,1


COMMENTS

Jacques Touchard proved in 1933 that for the Bell numbers (A000110), Bell(p+k) == Bell(k+1) + Bell(k) (mod p) for all primes p and k >= 0.
a(0)=21361 is the smallest pseudoprime of the congruence Bell(p) == 2(mod p). It was found by W. F. Lunnon and verified to be the smallest by David W. Wilson in 2007 (see comment in A000110).
a(84) is the first term that is larger than a(0).


REFERENCES

J. Touchard, "Propriétés arithmétiques de certains nombres récurrents", Ann. Soc. Sci. Bruxelles A 53 (1933), pp. 2131.


LINKS



EXAMPLE

a(1)=8 since 8 is composite, yet Bell(8+1)Bell(1)Bell(2) = 21144 = 8 * 3 * 881 is divisible by 8


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



