A260210 - OEIS

A260210

A034602(n) modulo prime(n).

1, 5, 1, 1, 3, 9, 13, 11, 1, 11, 34, 33, 31, 38, 58, 56, 24, 35, 62, 38, 23, 27, 96, 84, 2, 66, 106, 74, 10, 31, 8, 34, 58, 26, 26, 144, 150, 140, 167, 137, 31, 107, 78, 157, 1, 103, 165, 97, 111, 60, 196, 48, 97, 259, 155, 175, 244, 13, 269, 34, 184, 222, 54

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,2

COMMENTS

p is a Wolstenholme prime (A088164) iff a(n) = 0. This holds for n = 1944 and n = 157504.

When performing a search for Wolstenholme primes, one can choose an integer constant c >= 0 and record all primes with a(n) <= c in order to get a larger data set.

The values here appear to have a nicer asymptotic growth behavior than those in A260209.

It appears that A260209(n)/a(n) = A001248(n).

The formula only returns integers for primes greater than 3. - Robert G. Wilson v, Jul 29 2015

LINKS

Felix Fröhlich, Table of n, a(n) for n = 3..10000

FORMULA

A034602(n)/prime(n) = A260209(n)/prime(n)^2, for n>2. - Robert G. Wilson v, Jul 29 2015

MATHEMATICA

f[n_] := Block[{p = Prime@ n}, (Mod[ Binomial[2p - 1, p - 1], p^4] - 1)/p^3]; Array[f, 60, 3] (* Robert G. Wilson v, Jul 29 2015 *)

PROG

(PARI) a(n) = p=prime(n); lift(Mod(binomial(2*p-1, p-1)\p^3, p))

CROSSREFS

Cf. A034602, A088164, A241014, A244801, A250406, A258367, A260209.

Sequence in context: A154740 A179261 A154567 * A139391 A196612 A110635

Adjacent sequences: A260207 A260208 A260209 * A260211 A260212 A260213

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Jul 19 2015

STATUS

approved