A291921 Numbers that are the sum of (at least two) consecutive primes in exactly three ways.

240, 287, 340, 371, 510, 660, 803, 864, 931, 961, 990, 1012, 1060, 1099, 1104, 1151, 1236, 1313, 1367, 1392, 1524, 1643, 1710, 1788, 1793, 1951, 1956, 2040, 2303, 2304, 2387, 2393, 2436, 2507, 2556, 2586, 2647, 2670, 2689, 2706, 2886, 3010, 3166, 3232, 3263

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Prime Sums

Example

240 is in the sequence because it can be written in exactly three ways as a sum of consecutive primes: 113 + 127, 53 + 59 + 61 + 67, and 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43.

Prog

(Magma) lst1:=[]; lst3:=[]; r:=3263; s:=PrimesUpTo(Floor(r-r/3)); t:=#s; y:=0; w:=0; z:=1; while y le r do y+:=NthPrime(z); w+:=1; z+:=1; end while; for q in [1..NthPrime(w-1)] do for a in [1..t-q] do c:=&+[s[b]: b in [a..a+q]]; if c gt r then break; else Append(~lst1, c); end if; end for; end for; lst2:=Sort(lst1); x:=#lst2; for n in [1..r] do d:=Position(lst2, n); if d ge 1 and d+2 le x then e:=[lst2[f]: f in [d..d+2]]; if Min(e) eq Max(e) then if d+3 gt x then Append(~lst3, n); else if not lst2[d+3] eq n then Append(~lst3, n); end if; end if; end if; end if; end for; lst3;

Crossrefs

Cf. A054998, A067373.

Sequence in context: A135194 A031173 A067373 * A257413 A030638 A179644

Adjacent sequences: A291918 A291919 A291920 * A291922 A291923 A291924

Keyword

nonn

Author

Arkadiusz Wesolowski, Sep 05 2017

Status

approved