Robert A. J. Matthews - cp's OEIS frontend

User: Robert A. J. Matthews

Robert A. J. Matthews has authored 2 sequences.

A000355 Primes p == 3, 9, 11 (mod 20) such that 2p+1 is also prime.

3, 11, 23, 29, 83, 89, 131, 191, 251, 431, 443, 491, 509, 683, 743, 809, 911, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1451, 1511, 1583, 1811, 1889, 1931, 2003, 2063, 2069, 2129, 2351, 2543, 2549, 2903, 2963, 2969, 3023, 3329, 3389, 3449, 3491, 3623, 3803

Offset: 1

Robert A. J. Matthews

a(n) = (A000353(n)-1)/2. - Reinhard Zumkeller, Feb 10 2009

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.

Subset of A005384.

Cf. A000353.

q:= p-> irem(p, 20) in {3, 9, 11} and andmap(isprime, [p,2*p+1]):
select(q, [$1..10000])[];  # Alois P. Heinz, Oct 31 2023

Select[Prime[Range[1000]], MatchQ[Mod[#, 20], 3|9|11] && PrimeQ[2#+1]&] (* Jean-François Alcover, Feb 07 2016 *)

is(n)=my(k=n%20); (k==3||k==9||k==11) && isprime(2*n+1) && isprime(n) \\ Charles R Greathouse IV, Nov 20 2014

More terms from Reinhard Zumkeller, Feb 10 2009

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

Original entry on oeis.org

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

Robert A. J. Matthews

nonn

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

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.

Subset of A005385.

Subsequence of A001913, A006883.

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

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

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

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

More terms from Reinhard Zumkeller, Feb 10 2009

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User: Robert A. J. Matthews

A000355 Primes p == 3, 9, 11 (mod 20) such that 2p+1 is also prime.

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