

A361259


a(n) is the least semiprime that is the sum of n consecutive primes.


1



10, 26, 39, 358, 58, 77, 155, 129, 583, 562, 323, 326, 551, 381, 629, 501, 707, 1294, 789, 791, 961, 1354, 1159, 1262, 1369, 1371, 1591, 1718, 1849, 1851, 2271, 2127, 3561, 2427, 3077, 2747, 3085, 3442, 4811, 3826, 3829, 3831, 5089, 4227, 4659, 4661, 5345, 7318, 5587, 8146, 6333, 6081, 6338
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OFFSET

3,1


COMMENTS

No sum of two consecutive primes is a semiprime. Proof: if prime(k) and prime(k+1) are odd primes, prime(k)+prime(k+1) is even, so the only way it could be a semiprime is for (prime(k)+prime(k+1))/2 to be prime. But this is impossible because prime(k) and prime(k+1) are consecutive primes and (prime(k)+prime(k+1))/2 is between them.


LINKS



EXAMPLE

a(3) = 10 = 2+3+5, a(4) = 26 = 3+5+7+11, a(5) = 39 = 3+5+7+11+13, a(6) = 358 = 47+53+59+61+67+71.


MAPLE

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
S:= ListTools:PartialSums(P):
f:= proc(n) local k, s;
if numtheory:bigomega(S[n])=2 then return S[n] fi;
if n::even then
for k from 1 do
if isprime((S[n+k]S[k])/2) then return S[n+k]S[k] fi
od
else
for k from 1 do
if numtheory:bigomega(S[n+k]S[k]) = 2 then return S[n+k]S[k] fi
od
fi
end proc:
map(f, [$3..100]);


MATHEMATICA

pr = Prime[Range[10^6]]; Do[to = Total /@ Partition[pr, n, 1]; se =
Select[to, 2 == PrimeOmega[#] &, 1][[1]]; AppendTo[s, se], {n, 3, 30}]; s


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



