A133784 -id:A133784 - cp's OEIS frontend

A154587 Numbers that can be expressed both as the sum of first prime numbers and as the sum of first nonprime numbers.

0, 5, 28, 71208, 74139, 9260197734, 12374540078, 7574780746329, 11101148723618, 102581905748236, 3325997869054417, 2886018916559052244845, 46437379006448216748610, 120197329614203475099994

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Jan 15 2009

Is this sequence finite?
Intersection of A007504 and A053767 generates A294174. - R. J. Mathar, Jan 17 2009
Heuristically, the sequence is infinite with about 2 sqrt(log x) members up to x. - Charles R Greathouse IV, Aug 14 2013

			5 = 2+3 = 1+4. 28 = 2+3+5+7+11 = 1+4+6+8+9.

Giovanni Resta, C program

Intersection of A007504 and A051349. - R. J. Mathar, Jan 17 2009

Cf. A133784, A294174.

P:=proc(q) local a,b,c,d,n; a:=0; b:=0; c:=0; d:=0; print(a);
for n from 1 to q do b:=nextprime(b); a:=a+b;
while cPaolo P. Lava, Feb 23 2018

With[{p = Prime@ Range[10^7]}, {0}~Join~Intersection[Accumulate@ p, Accumulate@ Complement[Range@ Max@ p, p]]] (* Michael De Vlieger, Feb 25 2018 *)

Corrected definition and a(6)-a(7) from R. J. Mathar, Jan 17 2009
a(8)-a(11) from Donovan Johnson, Feb 19 2009
a(12)-a(14) from Giovanni Resta, Aug 14 2013
Edited and a(1)=0 prepended by Max Alekseyev, Feb 10 2018

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.

Original entry on oeis.org

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

Offset: 1

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

nonn

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

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

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

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 *)

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

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

cp's OEIS Frontend

A154587 Numbers that can be expressed both as the sum of first prime numbers and as the sum of first nonprime numbers.

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