A283869 Primes p such that p+12, (p+1)/2, and (p+13)/2 are also prime.

61, 661, 1201, 4261, 5101, 6121, 6361, 12421, 12541, 12841, 13921, 15361, 17041, 18301, 19801, 21661, 26821, 31321, 36901, 47521, 54121, 55921, 56101, 71341, 80701, 83221, 87421, 91381, 101161, 107761, 109441, 126481, 128461, 129841, 131101, 135601, 146941, 151141, 151561

Offset

1,1

Comments

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

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).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

Example

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

Mathematica

Select[Range@ 160000, Mod[#, 60] == 1 && PrimeQ[#] && PrimeQ[# + 12] && PrimeQ[(# + 1)/2] && PrimeQ[(# + 13)/2] &] (* Indranil Ghosh, Mar 17 2017 *)
Select[Range[1, 152000, 60], AllTrue[{#, #+12, (#+1)/2, (#+13)/2}, PrimeQ]&] (* Harvey P. Dale, Oct 14 2021 *)

Prog

(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
(Python)
from sympy import isprime
[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

Crossrefs

Cf. A005383.

Sequence in context: A068850 A142667 A317462 * A173805 A092571 A119597

Adjacent sequences: A283866 A283867 A283868 * A283870 A283871 A283872

Keyword

nonn

Author

Altug Alkan, Mar 17 2017, after Zak Seidov's comment in A005383

Status

approved