A331808 Composite numbers of the form 2*p + q, where p, q are consecutive prime numbers.

25, 35, 75, 99, 115, 125, 133, 147, 165, 189, 205, 215, 225, 255, 275, 295, 305, 323, 385, 399, 413, 427, 459, 477, 493, 507, 525, 539, 553, 575, 583, 609, 645, 705, 759, 777, 795, 819, 835, 845, 893, 925, 935, 943, 965, 999, 1043, 1065, 1085, 1107, 1125, 1141, 1155, 1175, 1195

Offset

1,1

Comments

An observation on the distribution of:

(a(n) mod 10) == 1 or 3 or 5 or 7 or 9

Up to 10^4 there are 99, 168, 373, 154, 222

Up to 10^5 there are 957, 1400, 2818, 1346, 1792

Up to 10^6 there are 9344, 12420, 22393, 11325, 14426

Up to 10^7 there are 85861, 109663, 185718, 100314, 122166

Up to 10^8 there are 792654, 968615, 1593058, 896008, 1059557

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

Odd number 75 is a term, because 75 = 2*23 + 29 and 23, 29 are consecutive prime numbers.

Maple

P:= [seq(ithprime(i), i=1..100)]:
remove(isprime, map(`*`, P[1..-2], 2)+P[2..-1]); # Robert Israel, Feb 17 2020

Mathematica

Select[Map[2 #1 + #2 & @@ # &, Partition[Prime@ Range@ 79, 2, 1]], CompositeQ] (* Michael De Vlieger, Jan 26 2020 *)

Prog

(PARI) forprime(p = 2, 500, c = 2*p + nextprime(p+1); if(!isprime(c), print(c", ")))

Crossrefs

Sequence in context: A063149 A046423 A347612 * A153446 A039457 A243749

Adjacent sequences: A331805 A331806 A331807 * A331809 A331810 A331811

Keyword

nonn

Author

Dimitris Valianatos, Jan 26 2020

Status

approved