A151744 -id:A151744 - 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

A060339 Primes that are each the sum of two, three, and four consecutive composite numbers.

Original entry on oeis.org

311, 337, 1009, 1103, 1511, 1777, 3671, 3889, 4271, 4657, 5737, 6841, 7561, 9649, 9769, 10223, 12239, 12889, 14759, 14831, 17401, 17569, 17783, 19009, 19031, 20903, 21529, 22369, 22751, 23279, 24049, 24889, 25057, 26423, 28871, 30671

Offset: 1

Robert G. Wilson v, Mar 30 2001

nonn

			A(2)= 377 is equal to 168+169 = 111+112+114 = 82+84+85+86.

Klaus Brockhaus, Table of n, a(n) for n=1..1000. [From _Klaus Brockhaus_, Jun 17 2009]

Cf. A151744. [From Klaus Brockhaus, Jun 17 2009]

composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); a = b = c = {}; Do[ p = Sum[ composite[ n + m ], {m, 0, 1} ]; If[ PrimeQ[ p ], a = Append[ a, p ] ]; p = Sum[ composite[ n + m ], {m, 0, 2} ]; If[ PrimeQ[ p ], b = Append[ b, p ] ]; p = Sum[ composite[ n + m ], {m, 0, 3} ]; If[ PrimeQ[ p ], c = Append[ c, p ] ], {n, 1, 25000} ]; Intersection[ a, b, c ]
Module[{cmp=Select[Range[20000],CompositeQ],c2,c3,c4},c2=Total/@ Partition[ cmp,2,1];c3=Total/@Partition[cmp,3,1];c4=Total/@ Partition[ cmp,4,1];Select[ Intersection[c2,c3,c4],PrimeQ]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 01 2020 *)

Definition clarified by Harvey P. Dale, Jul 01 2020

cp's OEIS Frontend

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

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