A000353 Primes p == 7, 19, 23 (mod 40) such that (p-1)/2 is also prime.

7, 23, 47, 59, 167, 179, 263, 383, 503, 863, 887, 983, 1019, 1367, 1487, 1619, 1823, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2903, 3023, 3167, 3623, 3779, 3863, 4007, 4127, 4139, 4259, 4703, 5087, 5099, 5807, 5927, 5939, 6047, 6659, 6779, 6899, 6983, 7247

Offset

1,1

Comments

The decimal expansion of 1/a(n) will produce a stream of a(n)-1 pseudo-random digits. - Reinhard Zumkeller, Feb 10 2009

The condition in the name is sufficient for primes p such that the decimal expansion of 1/p recurs after p-1 digits, which is the maximum-possible cycle length. - Robert A. J. Matthews, Oct 31 2023

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Robert A. J. Matthews, Maximally periodic reciprocals, Bull. Institute of Mathematics and Its Applications, vol. 28, p. 147-148, 1992.

Wikipedia, Sophie Germain prime

Index entries for sequences related to decimal expansion of 1/n.

Formula

a(n) = 2*A000355(n)+1. - Reinhard Zumkeller, Feb 10 2009

Maple

q:= p-> irem(p, 40) in {7, 19, 23} and andmap(isprime, [p, (p-1)/2]):
select(q, [$1..10000])[];  # Alois P. Heinz, Oct 31 2023

Mathematica

Select[Prime[Range[1000]], MatchQ[Mod[#, 40], 7|19|23] && PrimeQ[(#-1)/2]&] (* Jean-François Alcover, Feb 07 2016 *)

Prog

(PARI) is(n)=my(k=n%40); (k==7||k==19||k==23) && isprime(n\2) && isprime(n) \\ Charles R Greathouse IV, Nov 20 2014

Crossrefs

Subset of A005385.

Subsequence of A001913, A006883.

Sequence in context: A031371 A176557 A370643 * A097149 A185007 A308732

Adjacent sequences: A000350 A000351 A000352 * A000354 A000355 A000356

Keyword

nonn

Author

Robert A. J. Matthews

Extensions

More terms from Reinhard Zumkeller, Feb 10 2009

Status

approved