cp's OEIS Frontend

A309770 Numbers that are sums of one or more consecutive primes in more than one way.

%I A309770 #14 Feb 16 2025 08:33:55
%S A309770 5,17,23,31,36,41,53,59,60,67,71,72,83,90,97,100,101,109,112,119,120,
%T A309770 127,131,138,139,143,152,173,180,181,187,197,199,204,210,211,221,223,
%U A309770 228,233,240,251,258,263,269,271,276,281,287,300,304,311,323,330,331,340,349
%N A309770 Numbers that are sums of one or more consecutive primes in more than one way.
%C A309770 Contains A067372 as a subsequence.
%H A309770 Robert Israel, <a href="/A309770/b309770.txt">Table of n, a(n) for n = 1..10000</a>
%H A309770 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>
%F A309770 A054845(a(n)) > 1.
%e A309770 5 is in the sequence because it can be written as either 5 or 2 + 3.
%e A309770 36 is the sequence because it can be written as either 5 + 7 + 11 + 13 or 17 + 19.
%p A309770 N:= 1000: # for terms <= N
%p A309770 P:= select(isprime, [2, seq(i,i=3..N,2)]):
%p A309770 S:= [0,op(ListTools:-PartialSums(P))]:
%p A309770 V:= Vector(N):
%p A309770 for i from 1 to nops(S) do
%p A309770   for j from i-1 to 1 by -1 do
%p A309770     v:= S[i]-S[j];
%p A309770     if v > N then break fi;
%p A309770     V[v]:= V[v]+1;
%p A309770 od od:
%p A309770 select(t -> V[t]>1, [$1..N]); # _Robert Israel_, Aug 22 2019
%Y A309770 Cf. A000040, A034707, A050936, A054845, A054996, A067372, A067377.
%K A309770 nonn
%O A309770 1,1
%A A309770 _Ilya Gutkovskiy_, Aug 16 2019