A067606 Primes p such that p+7 == 0 (mod phi(p+7)).

5, 11, 17, 29, 41, 47, 89, 101, 137, 281, 317, 479, 569, 641, 761, 857, 1289, 1451, 1721, 2297, 2909, 3449, 3881, 8741, 9209, 11657, 12281, 17489, 23321, 26237, 36857, 39359, 46649, 62201, 73721, 98297, 147449, 157457, 331769, 393209, 839801, 944777, 1119737

Offset: 1

Author

Benoit Cloitre, Feb 22 2002

Keywords

• nonn

Comments

Equivalently, these are the primes of form 2^(i+1)*3^j - 7. We empirically have log(a(n)) ~ 0.23...*n + O(1), but the constant seems difficult to compute precisely. - Matthew House, Aug 13 2024

Links

• Matthew House, Table of n, a(n) for n = 1..9949 (all primes proven via ECPP)

Crossrefs

Cf. A007694.

Programs

Mathematica

Select[Prime[Range[35000]],Divisible[#+7,EulerPhi[#+7]]&] (* Harvey P. Dale, Aug 15 2016 *)
lim = 10^7 + 7; Sort[Select[Flatten[Table[2^i*3^j - 7, {i, 1, Log2[lim]}, {j, 0, Log[3, lim/2^i]}]], # > 0 && PrimeQ[#] &]] (* Matthew House, Aug 13 2024 *)

Extensions

More terms from Matthew House, Aug 13 2024