A257035 Numbers m such that 6m+1, 12m+1, 18m+1, 36m+1 and 72m+1 are all prime.

1, 121, 380, 506, 511, 3796, 5875, 6006, 8976, 9025, 9186, 10920, 12245, 12896, 14476, 14800, 15386, 22451, 23471, 32326, 35175, 38460, 39536, 40420, 41456, 43430, 44415, 59901, 60076, 61341, 74676, 76615, 76986, 82530, 87390, 99486, 101101, 107926, 112315, 112840, 115101

Offset: 1

Author

M. F. Hasler, Apr 14 2015

Keywords

• nonn
• easy

Comments

A subsequence of A206024, which contains A206349 as a subsequence, see there for motivations.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A002997, A112428, A174613, A206024, A206349.

Programs

GAP

Filtered([1..120000],m->IsPrime(6*m+1) and IsPrime(12*m+1) and IsPrime(18*m+1) and IsPrime(36*m+1) and IsPrime(72*m+1)); # Muniru A Asiru, Jun 06 2018

Magma

[n: n in [0..2*10^5] | IsPrime(6*n+1) and IsPrime(12*n+1) and IsPrime(18*n+1) and IsPrime(36*n+1)and IsPrime(72*n+1)]; // Vincenzo Librandi, Apr 15 2015

Maple

f:=isprime: select(m->f(6*m+1) and f(12*m+1) and f(18*m+1) and f(36*m+1) and f(72*m+1),[$1..120000] ); # Muniru A Asiru, Jun 06 2018

Mathematica

Select[Range[120000], PrimeQ[6 # + 1] && PrimeQ[12 # + 1] && PrimeQ[18 # + 1] && PrimeQ[36 # + 1] && PrimeQ[72 # + 1] &] (* Vincenzo Librandi, Apr 15 2015 *)
Select[Range[120000],AllTrue[{6,12,18,36,72}#+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 23 2016 *)

PARI

is(m,c=72)=!until(bittest(c\=2,0)&&9>c+=3,isprime(m*c+1)||return)