A290163 Primes p such that A288814(4*p) - A288814(3*p) = 7.

2, 19, 29, 59, 79, 89, 131, 149, 151, 389, 479, 499, 521, 571, 631, 659, 701, 739, 919, 941, 971, 1069, 1279, 1289, 1361, 1381, 1451, 1471, 1489, 1669, 1949, 2069, 2089, 2131, 2549, 2609, 2749, 2791, 3011, 3109, 3181, 3251, 3361, 3389, 3539, 3581, 3659, 4049, 4091, 4139

Offset

1,1

Comments

Proper subset of A290164.

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.

Links

Table of n, a(n) for n=1..50.

Example

A288814(4*2) - A288814(3*2) = 15 - 8 = 7, therefore prime 2 is in the sequence;
A288814(4*19) - A288814(3*19) = 219 - 212 = 7, therefore prime 19 is a term.

Mathematica

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 *)

Crossrefs

Cf. A259730, A288814, A290164.

Sequence in context: A083689 A102617 A365235 * A284496 A120276 A006962

Adjacent sequences: A290160 A290161 A290162 * A290164 A290165 A290166

Keyword

nonn

Author

David James Sycamore, Jul 22 2017

Extensions

More terms from Altug Alkan, Jul 23 2017

Edited by Robert Israel, Jul 24 2017

Status

approved