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.

%I A154587 #37 Mar 06 2018 11:16:20
%S A154587 0,5,28,71208,74139,9260197734,12374540078,7574780746329,
%T A154587 11101148723618,102581905748236,3325997869054417,
%U A154587 2886018916559052244845,46437379006448216748610,120197329614203475099994
%N A154587 Numbers that can be expressed both as the sum of first prime numbers and as the sum of first nonprime numbers.
%C A154587 Is this sequence finite?
%C A154587 Intersection of A007504 and A053767 generates A294174. - _R. J. Mathar_, Jan 17 2009
%C A154587 Heuristically, the sequence is infinite with about 2 sqrt(log x) members up to x. - _Charles R Greathouse IV_, Aug 14 2013
%H A154587 Giovanni Resta, <a href="/A154587/a154587.c.txt">C program</a>
%e A154587 5 = 2+3 = 1+4. 28 = 2+3+5+7+11 = 1+4+6+8+9.
%p A154587 P:=proc(q) local a,b,c,d,n; a:=0; b:=0; c:=0; d:=0; print(a);
%p A154587 for n from 1 to q do b:=nextprime(b); a:=a+b;
%p A154587 while c<a do d:=d+1; if not isprime(d) then c:=c+d; fi; od;
%p A154587 if c=a then print(a); fi; od; end: P(10^9);# _Paolo P. Lava_, Feb 23 2018
%t A154587 With[{p = Prime@ Range[10^7]}, {0}~Join~Intersection[Accumulate@ p, Accumulate@ Complement[Range@ Max@ p, p]]] (* _Michael De Vlieger_, Feb 25 2018 *)
%Y A154587 Intersection of A007504 and A051349. - _R. J. Mathar_, Jan 17 2009
%Y A154587 Cf. A133784, A294174.
%K A154587 nonn,more,nice
%O A154587 1,2
%A A154587 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jan 15 2009
%E A154587 Corrected definition and a(6)-a(7) from _R. J. Mathar_, Jan 17 2009
%E A154587 a(8)-a(11) from _Donovan Johnson_, Feb 19 2009
%E A154587 a(12)-a(14) from _Giovanni Resta_, Aug 14 2013
%E A154587 Edited and a(1)=0 prepended by _Max Alekseyev_, Feb 10 2018