A151745 -id:A151745 - cp's OEIS frontend

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

Claudio Meller, Jun 15 2009

nonn

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

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

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).

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 *)

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

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

A151741 Composite which are the sum of three consecutive composite numbers.

Original entry on oeis.org

18, 27, 36, 45, 49, 54, 63, 75, 78, 81, 85, 90, 95, 99, 102, 105, 117, 121, 126, 135, 143, 147, 150, 153, 161, 165, 168, 171, 175, 180, 185, 189, 192, 195, 203, 207, 216, 221, 225, 228, 231, 235, 243, 247, 255, 258, 261, 265, 273, 276, 279, 282, 285, 289, 297

Offset: 1

Claudio Meller, Jun 15 2009

nonn

Cf. A151740-A151745, A060254, A060327, A060339, A096785, A096787, A135170.

Module[{c=Select[Range[300],CompositeQ],s3},s3=Total/@Partition[c,3,1];Intersection[c,s3]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 27 2019 *)

c1=4;c2=6;for(c3=8,299,isprime(c3) && next;isprime(c1+c2+c3) || print1(c1+c2+c3",");c1=c2;c2=c3) \\ M. F. Hasler, Jun 16 2009

A161689 Intersection of A151740 and A151741.

Original entry on oeis.org

49, 99, 153, 161, 171, 175, 185, 189, 221, 231, 235, 243, 247, 265, 285, 289, 319, 329, 341, 351, 369, 375, 391, 405, 429, 435, 441, 469, 473, 495, 507, 517, 531, 535, 545, 549, 581, 589, 603, 609, 639, 645, 651, 657, 667, 671, 679, 689, 711, 715, 725, 729

Offset: 1

Zak Seidov, Jun 17 2009

nonn

Composite numbers that are sum of two and three consecutive composite numbers. Provably only odd integers.

			49=24+25=15+16+18
99=49+50=32+33+34
153=76+77=50+51+52.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

A151740, A151741, A151745.

Module[{c=Select[Range[800],CompositeQ],s2,s3},s2=Total/@Partition[c,2,1];s3=Total/@Partition[c,3,1];Intersection[c,s2,s3]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 27 2019 *)

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

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A151741 Composite which are the sum of three consecutive composite numbers.

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A161689 Intersection of A151740 and A151741.

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