A135363 Sums of two or more consecutive semiprimes.

10, 15, 19, 24, 25, 29, 33, 36, 39, 43, 47, 48, 50, 51, 54, 58, 59, 60, 67, 68, 69, 72, 73, 75, 77, 79, 82, 83, 84, 85, 91, 93, 94, 95, 97, 100, 101, 102, 106, 107, 109, 112, 115, 116, 118, 120, 122, 123, 126, 127, 128, 133, 134, 140, 142, 143, 146, 148, 151, 152

Offset

1,1

Comments

This is to A050936 as A001358 is to A000040.

Links

Table of n, a(n) for n=1..60.

Example

a(1) = 10 = 4 + 6.
a(2) = 15 = 6 + 9.
a(3) = 19 = 9 + 10 = 4 + 6 + 9.
a(4) = 24 = 10 + 14.
a(5) = 25 = 6 + 9 + 10.
a(6) = 29 = 14 + 15 = 4 + 6 + 9 + 10.
a(7) = 33 = 9 + 10 + 14.
a(8) = 36 = 15 + 21.
a(9) = 39 = 10 + 14 + 15.
a(10) = 43 = 21 + 22.

Maple

isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true; else false ; fi ; end: A001358 := proc(n) option remember ; local a; if n <= 3 then op(n, [4, 6, 9]) ; else a := A001358(n-1)+1 ; while not isA001358(a) do a := a+1 ; od ; RETURN(a) ; fi ; end: isA135363 := proc(n) local frst, lst, psum ; for frst from 1 do if A001358(frst) >= n then RETURN(false) ; fi ; for lst from frst+1 do psum := add(A001358(k), k=frst..lst) ; if psum = n then RETURN(true) ; elif psum > n then break ; fi ; od: od: end: for n from 4 to 200 do if isA135363(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, Dec 11 2007

Mathematica

okQ[n_] := With[{SP = Select[Range[n], PrimeOmega[#] == 2 &]}, Select[IntegerPartitions[n, {2, Infinity}, SP], SequencePosition[SP, Reverse@#] != {}&]] != {};
Reap[For[k = 10, k < 200, k++, If[okQ[k], Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Jan 29 2024 *)

Crossrefs

Cf. A000040, A001358, A050936.

Sequence in context: A139540 A343550 A285176 * A118717 A181529 A232501

Adjacent sequences: A135360 A135361 A135362 * A135364 A135365 A135366

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 09 2007

Extensions

Corrected and extended by R. J. Mathar, Dec 11 2007

Status

approved