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A054998 Integers that can be expressed as the sum of consecutive primes in exactly 3 ways. 8
41, 83, 197, 199, 223, 240, 251, 281, 287, 340, 371, 401, 439, 491, 510, 593, 660, 733, 803, 857, 864, 883, 931, 941, 961, 983, 990, 991, 1012, 1060, 1061, 1099, 1104, 1187, 1236, 1283, 1313, 1361, 1381, 1392, 1433, 1439, 1493, 1511, 1523, 1524, 1553 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, section C2.
LINKS
Carlos Rivera, Puzzle 46. Primes expressible as sum of consecutive primes in K ways, The Prime Puzzles and Problems Connection.
FORMULA
A054845(a(n)) = 3. - Ray Chandler, Sep 20 2023
EXAMPLE
41 can be expressed as 41 or 11+13+17 or 2+3+5+7+11+13, so 41 is in the sequence.
MAPLE
N:= 10^4: # to get all terms <= N
P:= [0, op(select(isprime, [2, seq(i, i=3..N, 2)]))]:
nP:= nops(P);
S:= ListTools:-PartialSums(P):
V:= Vector(N):
for i from 1 to nP-1 do
for j from i+1 to nP while S[j] - S[i] <= N do
V[S[j]-S[i]]:= V[S[j]-S[i]]+1
od od:
select(t -> V[t] = 3, [$1..N]): # Robert Israel, Apr 05 2017
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A136072 A098061 A141898 * A067378 A331031 A171138
KEYWORD
nonn
AUTHOR
Jud McCranie, May 30 2000
STATUS
approved

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)