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A154587
Numbers that can be expressed both as the sum of first prime numbers and as the sum of first nonprime numbers.
4
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
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
Sequence in context: A125137 A348350 A132550 * A374602 A083020 A033503
KEYWORD
nonn,more,nice
AUTHOR
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