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

1,2

Comments

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

Links

Table of n, a(n) for n=1..14.

Giovanni Resta, C program

Example

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

Maple

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 c<a do d:=d+1; if not isprime(d) then c:=c+d; fi; od;
if c=a then print(a); fi; od; end: P(10^9); # Paolo P. Lava, Feb 23 2018

Mathematica

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

Crossrefs

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

Cf. A133784, A294174.

Sequence in context: A125137 A348350 A132550 * A083020 A033503 A181616

Adjacent sequences: A154584 A154585 A154586 * A154588 A154589 A154590

Keyword

nonn,more,nice

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 15 2009

Extensions

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

Status

approved