A154588 Numbers that can be expressed as the sum of the first j integer numbers or the first k nonprime numbers, with j and k >=1.

1, 28, 435, 10296, 415416, 1062153, 3703281, 426626655, 782002378, 102886232631, 1636197988776, 2749764593278, 61972139524851, 813577626225078, 1604393353172781, 3603538956517305, 44000970048906445, 83556903098276790, 208955344344897381

Offset: 1

Author

Paolo P. Lava & Giorgio Balzarotti, Jan 16 2009, Jan 19 2009

Keywords

• nonn

Comments

The indices (j,k) where A000217(j) = A051349(k) are (1,1), (7,5), (29,23), (143,123), (911,823), (1457,1327), (2721,2501), (29210,27488), (39547,37295) , (453621,433381) , (1808976,1737137) , (2345107,2253859) , (11133026,10746793), (40338012,39053670), (56646153,54880858) , (84894510,82314170) , (296651209,288273745), (408795555,397457085), (646460121,628975505). - Donovan Johnson, Sep 11 2009

Examples

			28 = A000217(7) = A051349(5).
435 = A000217(19) = A051349(23).
10296 = A000217(143) = A051349(123).
		

Crossrefs

Cf. A007504, A051349, A066527, A133784, A154587.

Programs

Mathematica

Module[{nn=10^7,np},np=Select[Range[nn],!PrimeQ[#]&];Intersection[Accumulate[Range[ nn]],Accumulate[ np]]] (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Feb 08 2024 *)

Formula

(A000217 INTERSECT A051349) MINUS {0}. - R. J. Mathar, Jan 21 2009

Extensions

10256 replaced with 10296 and two more terms added by R. J. Mathar, Jan 21 2009

Extended beyond a(9) by Donovan Johnson, Sep 11 2009