A283869 - OEIS

%I #20 Sep 15 2022 03:46:23

%S 61,661,1201,4261,5101,6121,6361,12421,12541,12841,13921,15361,17041,

%T 18301,19801,21661,26821,31321,36901,47521,54121,55921,56101,71341,

%U 80701,83221,87421,91381,101161,107761,109441,126481,128461,129841,131101,135601,146941,151141,151561

%N Primes p such that p+12, (p+1)/2, and (p+13)/2 are also prime.

%C Numbers k such that both k and k + 12 are terms of A005383.

%C All terms are of the form 60*m + 1 for m > 0 since A005383(i) == 1 (mod 12) for i > 2 and if A005383(i) + 12 is a term in A005383, then A005383(i) == 1 (mod 10).

%H Charles R Greathouse IV, <a href="/A283869/b283869.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) == 1 (mod 60).

%e 61 is a term because 61 and 73 are both terms in A005383.

%t Select[Range@ 160000, Mod[#, 60] == 1 && PrimeQ[#] && PrimeQ[# + 12] && PrimeQ[(# + 1)/2] && PrimeQ[(# + 13)/2] &] (* _Indranil Ghosh_, Mar 17 2017 *)

%t Select[Range[1,152000,60],AllTrue[{#,#+12,(#+1)/2,(#+13)/2},PrimeQ]&] (* _Harvey P. Dale_, Oct 14 2021 *)

%o (PARI) is(n)=n%60==1 && isprime(n) && isprime(n+12) && isprime((n+1)/2) && isprime((n+13)/2) \\ _Charles R Greathouse IV_, Mar 17 2017

%o (Python)

%o from sympy import isprime

%o [i for i in range(1, 160001) if i%60 == 1 and isprime(i) and isprime(i + 12) and isprime((i + 1)/2) and isprime((i + 13)/2)] # _Indranil Ghosh_, Mar 17 2017

%Y Cf. A005383.

%K nonn

%O 1,1

%A _Altug Alkan_, Mar 17 2017, after _Zak Seidov_'s comment in A005383