A151740 Composites that are the sum of two consecutive composite numbers.

10, 14, 22, 26, 34, 38, 46, 49, 51, 55, 58, 62, 65, 69, 74, 77, 82, 86, 91, 94, 99, 106, 111, 115, 118, 122, 125, 129, 134, 142, 146, 153, 155, 158, 161, 166, 169, 171, 175, 178, 183, 185, 187, 189, 194, 202, 206, 209, 214, 218, 221, 226, 231, 235, 237, 243, 245

Offset: 1

Author

Claudio Meller, Jun 15 2009

Keywords

• nonn

Comments

The even terms of this sequence are exactly twice the primes > 3. The odd terms are odd composites c for which the odd integer next to c/2 is not prime. - M. F. Hasler, Jun 16 2009

The English language can be ambiguous! What is meant here is: write down a list of the composite numbers 4,6,8,9,10,12,... Whenever the sum of two adjacent terms is composite, adjoin it to the sequence: 4+6=10, 6+8=14, 10+12=22, ... - N. J. A. Sloane, Nov 26 2019

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A151741, A151742, A151743, A151744, A151745, A060254, A060327, A060339, A096785, A096787, A135170. - M. F. Hasler, Jun 16 2009

Cf. A167611 (Essentially the same, except for initial term).

Programs

Mathematica

CompositeNext[n_]:=Module[{k=n+1},While[PrimeQ[k],k++ ];k]; q=6!;lst2={};Do[If[ !PrimeQ[n],c=CompositeNext[n];a2=n+c;If[ !PrimeQ[a2],AppendTo[lst2,a2]]],{n,q}];lst2 (* Vladimir Joseph Stephan Orlovsky, Jun 17 2009 *)
Module[{c=Select[Range[300],CompositeQ],s2},s2=Total/@Partition[c,2,1];Intersection[c,s2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 27 2019 *)

PARI

isA151740(n)= bittest(n,0) || return(isprime(n/2) && n>6); !isprime(bitor(n\2,1)) && !isprime(n) && n>1 \\ M. F. Hasler, Jun 16 2009

Python

from sympy import isprime, composite
print([totest for k in range(1,92) if not isprime(totest := composite(k) + composite(k+1))]) # Karl-Heinz Hofmann, Feb 06 2024