A000353 - OEIS

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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

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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 *)