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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.
0
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
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
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