cp's OEIS Frontend

A054998 Integers that can be expressed as the sum of consecutive primes in exactly 3 ways.

%I A054998 #24 Sep 20 2023 15:58:08
%S A054998 41,83,197,199,223,240,251,281,287,340,371,401,439,491,510,593,660,
%T A054998 733,803,857,864,883,931,941,961,983,990,991,1012,1060,1061,1099,1104,
%U A054998 1187,1236,1283,1313,1361,1381,1392,1433,1439,1493,1511,1523,1524,1553
%N A054998 Integers that can be expressed as the sum of consecutive primes in exactly 3 ways.
%D A054998 R. K. Guy, Unsolved Problems in Number Theory, section C2.
%H A054998 Robert Israel, <a href="/A054998/b054998.txt">Table of n, a(n) for n = 1..10000</a>
%H A054998 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_046.htm">Puzzle 46. Primes expressible as sum of consecutive primes in K ways</a>, The Prime Puzzles and Problems Connection.
%F A054998 A054845(a(n)) = 3. - _Ray Chandler_, Sep 20 2023
%e A054998 41 can be expressed as 41 or 11+13+17 or 2+3+5+7+11+13, so 41 is in the sequence.
%p A054998 N:= 10^4: # to get all terms <= N
%p A054998 P:= [0,op(select(isprime, [2,seq(i,i=3..N,2)]))]:
%p A054998 nP:= nops(P);
%p A054998 S:= ListTools:-PartialSums(P):
%p A054998 V:= Vector(N):
%p A054998 for i from 1 to nP-1 do
%p A054998   for j from i+1 to nP while S[j] - S[i] <= N do
%p A054998      V[S[j]-S[i]]:= V[S[j]-S[i]]+1
%p A054998 od od:
%p A054998 select(t -> V[t] = 3, [$1..N]): # _Robert Israel_, Apr 05 2017
%t A054998 Module[{nn = 300, s}, s = Array[Prime, nn]; Keys@ Take[Select[KeySort@ Merge[Table[PositionIndex@ Map[Total, Partition[s, k, 1]], {k, nn/2}], Identity], Length@ # == 3 &], Floor[nn/6]]] (* _Michael De Vlieger_, Apr 06 2017, Version 10 *)
%Y A054998 Cf. A054845, A054859, A054996, A054997, A054999, A055500, A055001.
%K A054998 nonn
%O A054998 1,1
%A A054998 _Jud McCranie_, May 30 2000