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

1,2

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

Links

Table of n, a(n) for n=1..19.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A093974 A121803 A022656 * A125485 A054337 A009685

Adjacent sequences: A154585 A154586 A154587 * A154589 A154590 A154591

Keyword

nonn

Author

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

Status

approved