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A260210
A034602(n) modulo prime(n).
5
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
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
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))
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jul 19 2015
STATUS
approved