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

Author

Robert A. J. Matthews

Keywords

• nonn

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.

Crossrefs

Subset of A005385.

Subsequence of A001913, A006883.

Programs

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 *)

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

Formula

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

Extensions

More terms from Reinhard Zumkeller, Feb 10 2009