The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 Robert Israel, Table of n, a(n) for n = 3..10000 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 Cf. A001358. Sequence in context: A322972 A080059 A071348 * A055042 A044071 A186279 Adjacent sequences: A361256 A361257 A361258 * A361260 A361261 A361262 KEYWORD nonn AUTHOR Zak Seidov and Robert Israel, Mar 06 2023 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 18 18:14 EDT 2024. Contains 373486 sequences. (Running on oeis4.)