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A000353 Primes p == 7, 19, 23 (mod 40) such that (p-1)/2 is also prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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
Robert A. J. Matthews, Maximally periodic reciprocals, Bull. Institute of Mathematics and Its Applications, vol. 28, p. 147-148, 1992.
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: A319050 A031371 A176557 * A097149 A185007 A308732
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Reinhard Zumkeller, Feb 10 2009
STATUS
approved

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Last modified February 27 21:03 EST 2024. Contains 370378 sequences. (Running on oeis4.)