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A125854 Primes p with the property that p divides the Wolstenholme number A001008((p+1)/2). 6
3, 29, 37, 3373, 2001907169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that if prime p>3 divides A001008((p+1)/2) then it also divides A001008((p-3)/2).

Note that for a prime p, H([p/2]) == 2*(2^(-p(p-1))-1)/p^2 (mod p). Therefore a prime p divides the Wolstenholme number A001008((p+1)/2) if and only if 2^(-p(p-1)) == 1-p^2 (mod p^3) or, equivalently, 2^(p-1) == 1+p (mod p^2).

Disjunctive union of the sequences A154998 and A121999 that contain primes congruent respectively to 1,3 and 5,7 modulo 8. (Alekseyev)

No other terms below 10^11. (Alekseyev)

a(6) > 5.5*10^12. - Giovanni Resta, Apr 13 2017

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

a(1) = 3 because prime 3 divides A001008(2) = 3 and there is no p<3 that divides A001008((p+1)/2).

a(2) = 29 because 29 divides A001008(15) = 1195757; but there is no prime p (3<p<29) that divides A001008((p+1)/2).

CROSSREFS

Cf. A001008, A121999, A014566, A154998

Sequence in context: A055062 A086174 A178642 * A167278 A106979 A087209

Adjacent sequences:  A125851 A125852 A125853 * A125855 A125856 A125857

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk, Dec 11 2006

EXTENSIONS

Entry revised and a(5)=2001907169 provided by Max Alekseyev, Jan 18 2009

Edited by Max Alekseyev, Oct 13 2009

STATUS

approved

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Last modified June 24 08:22 EDT 2017. Contains 288697 sequences.