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A151740
Composites that are the sum of two consecutive composite numbers.
7
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
1,1
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
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 *)
PROG
(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
CROSSREFS
Cf. A167611 (Essentially the same, except for initial term).
Sequence in context: A319802 A244894 A167611 * A136802 A362866 A084278
KEYWORD
nonn
AUTHOR
Claudio Meller, Jun 15 2009
STATUS
approved