A290163 - OEIS

%I #34 Aug 21 2017 22:39:44

%S 2,19,29,59,79,89,131,149,151,389,479,499,521,571,631,659,701,739,919,

%T 941,971,1069,1279,1289,1361,1381,1451,1471,1489,1669,1949,2069,2089,

%U 2131,2549,2609,2749,2791,3011,3109,3181,3251,3361,3389,3539,3581,3659,4049,4091,4139

%N Primes p such that A288814(4*p) - A288814(3*p) = 7.

%C Proper subset of A290164.

%C Terms of A290164 not in this sequence include 5, 11, 61, 191, 431, 541, 1181, 3571, ... corresponding to primes p such that A(4*p) - A(3*p) = A(3*p) - 1, where A=A288814. Examples: A(4*5) - A(3*5) = 51 - 26 = 25; A(4*541) - A(3*541) = 6483 - 3242 = 3241.

%e A288814(4*2) - A288814(3*2) = 15 - 8 = 7, therefore prime 2 is in the sequence;

%e A288814(4*19) - A288814(3*19) = 219 - 212 = 7, therefore prime 19 is a term.

%t With[{s = Array[Boole[CompositeQ@ #] Total@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger[#]] &, 10^5]}, Select[Prime@ Range[600], Function[p, FirstPosition[s, _?(# == 4 p &)][[1]] - FirstPosition[s, _?(# == 3 p &)][[1]] == 7]]] (* _Michael De Vlieger_, Jul 23 2017 *)

%Y Cf. A259730, A288814, A290164.

%K nonn

%O 1,1

%A _David James Sycamore_, Jul 22 2017

%E More terms from _Altug Alkan_, Jul 23 2017

%E Edited by _Robert Israel_, Jul 24 2017