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

Author

Arkadiusz Wesolowski, Sep 05 2017

Keywords

• nonn

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Prime Sums

Crossrefs

Cf. A054998, A067373.

Programs

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;