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A291921 Numbers that are the sum of (at least two) consecutive primes in exactly three ways. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 05:25 EDT 2020. Contains 336290 sequences. (Running on oeis4.)