A111215 -id:A111215 - cp's OEIS frontend

A089986 Numbers n such that 4n + 7 is prime.

-1, 0, 1, 3, 4, 6, 9, 10, 13, 15, 16, 18, 19, 24, 25, 30, 31, 33, 36, 39, 40, 43, 46, 48, 51, 54, 55, 58, 61, 64, 66, 69, 75, 76, 81, 85, 88, 90, 93, 94, 103, 106, 108, 109, 114, 115, 118, 120, 121, 123, 124, 129, 135, 139, 141, 145, 148, 150, 153, 156, 159, 160, 163, 169

Offset: 1

Giovanni Teofilatto, Jan 13 2004

sign

M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.
Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997.

Cf. A005099 ((( Primes = -1 mod 4 ) + 1)/4), A005098 (4n+1 is prime), A095278 (4n+3 is prime), A111215 (4n+5 is prime).

[ n: n in [-1..170] | IsPrime(4*n+7) ];

A089986:=n->`if`(isprime(4*n+7), n, NULL): seq(A089986(n), n=-1..200); # Wesley Ivan Hurt, Sep 18 2014

Select[Range[-1, 200], PrimeQ[4 # + 7] &] (* Wesley Ivan Hurt, Sep 18 2014 *)

is(n)=isprime(4*n+7) \\ Charles R Greathouse IV, Feb 20 2017

a(n) = A005099(n) - 2 = A095278(n) - 1.

Edited and extended by Klaus Brockhaus, Dec 22 2008

A023214 Primes p such that 4*p + 5 is also prime.

Original entry on oeis.org

2, 3, 17, 23, 47, 59, 83, 101, 107, 113, 149, 167, 191, 233, 251, 257, 281, 311, 401, 443, 449, 467, 503, 521, 569, 593, 617, 647, 653, 677, 761, 827, 839, 857, 863, 881, 941, 947, 971, 1013, 1031, 1049, 1109, 1163, 1181, 1277, 1301, 1307, 1319, 1361, 1409, 1433

Offset: 1

David W. Wilson

nonn

Except for the first two terms, all terms are congruent to 5 (mod 6). - John Cerkan, Sep 07 2016

John Cerkan, Table of n, a(n) for n = 1..10000

Subsequence of A111215. - Michel Marcus, Jul 08 2016

[n: n in [0..100000] | IsPrime(n) and IsPrime(4*n+5)] // Vincenzo Librandi, Aug 04 2010

A023214:=n->`if`(isprime(n) and isprime(4*n+5), n, NULL): seq(A023214(n), n=1..3*10^3); # Wesley Ivan Hurt, Sep 07 2016

Select[Prime[Range[250]],PrimeQ[4#+5]&] (* Harvey P. Dale, Oct 21 2018 *)

A153085 Numbers k such that 4*k + 5 is not prime.

Original entry on oeis.org

1, 4, 5, 7, 10, 11, 13, 15, 16, 18, 19, 20, 22, 25, 28, 29, 30, 31, 32, 34, 35, 37, 39, 40, 41, 43, 45, 46, 49, 50, 51, 52, 53, 54, 55, 58, 60, 61, 62, 64, 65, 67, 70, 71, 73, 74, 75, 76, 79, 80, 81, 82, 84, 85, 88, 89, 90, 91, 93, 94, 95, 97, 100, 102, 103, 105, 106

Offset: 1

Vincenzo Librandi, Dec 18 2008

nonn

Let p=2n+1 be an odd number, then A140869(n,n) = (p^2-5)/4 = A028387(n-1).

One less than the associated entry in A045751: a(n) = A045751(n+1)-1. - R. J. Mathar, Jan 05 2011

			Triangle begins:
1;
*, 5;
4, *, 11;
*, 10, *, 19;
7, *, 18, *, 29;
*, 15, *, 28, *, 41;
where * mark the entries in A140869 which are non-integer if floor(.) is not applied there.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A028387, A045751, A111215, A140869.

[n: n in [1..120] | not IsPrime(4*n + 5)]; // Vincenzo Librandi, Oct 15 2012

Select[Range[200], !PrimeQ[4 # + 5] &] (* Vincenzo Librandi, Oct 15 2012 *)

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A089986 Numbers n such that 4n + 7 is prime.

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A023214 Primes p such that 4*p + 5 is also prime.

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A153085 Numbers k such that 4*k + 5 is not prime.

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