A348791 -id:A348791 - cp's OEIS frontend

A065867 Primes which are the sum of a prime number of consecutive primes.

5, 23, 31, 41, 53, 59, 67, 71, 83, 97, 101, 109, 131, 139, 173, 181, 197, 199, 211, 223, 233, 251, 263, 269, 271, 281, 311, 331, 349, 353, 373, 401, 421, 431, 439, 443, 449, 457, 463, 487, 491, 499, 503, 523, 563, 587, 593, 607, 617, 631, 647, 659, 661, 677

Offset: 1

Henry Bottomley, Dec 07 2001

			5 = 2 + 3.
23 = 5 + 7 + 11.
31 = 7 + 11 + 13.
41 = 11 + 13 + 17.
53 = 5 + 7 + 11 + 13 + 17.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001043, A034707, A034962, A034965, A138591, A348790, A348791.

Cf. A034962 (subsequence).

lst={};Do[s=Prime[m];k=1;Do[p=Prime[n];s+=p;k++;If[PrimeQ[s]&&PrimeQ[k],If[s<=10837,AppendTo[lst,s]]],{n,m+1,5*5!}],{m,5*5!}];lst=Take[Union@lst,500] (* Vladimir Joseph Stephan Orlovsky, Sep 13 2009 *)
Module[{nn=60,prs},prs=Prime[Range[nn]];Take[Select[Union[ Flatten[ Table[ Total/@ Partition[prs,n,1],{n,prs}]]],PrimeQ],nn]] (* Harvey P. Dale, Aug 12 2016 *)

A348790 a(n) is the smallest number that can be written as the sum of a prime number of consecutive primes in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

1, 5, 83, 371, 311, 455713, 2196879, 77494559

Offset: 0

Harvey P. Dale and N. J. A. Sloane, Nov 29 2021

Note that a(n) itself need not be a prime (compare A348791).

			a(2) = 83 from 83 = 11+13+17+19+23 (5 primes) = 23+29+31 (3 primes).
a(3) = 371 from 371 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 (13 primes) = 41 + 43 + 47 + 53 + 59 + 61 + 67 (7 primes) = 113 + 127 + 131 (3 primes). - _Michael S. Branicky_, Nov 30 2021
a(4) = 311 from
  311 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (11 primes)
  = 31 + 37 + 41 + 43 + 47 + 53 + 59 (7 primes)
  = 53 + 59 + 61 + 67 + 71 (5 primes)
  = 101 + 103 + 107 (3 primes).
The 7 ways to get a(7), written as [count, first prime in sum, last prime in sum, # of primes in sum]: [1, 233, 39551, 4111], [2, 42323, 58909, 1531], [3, 135899, 142381, 557], [4, 710321, 711691, 109], [5, 1061087, 1062073, 73], [6, 4558349, 4558633, 17], [7, 15498871, 15498971, 5]. - _Hugo Pfoertner_, Nov 30 2021

Cf. A082283. See A348791 for another version.

a(6)-a(7) from Hugo Pfoertner, Nov 30 2021

a(3) and a(5) corrected by Michael S. Branicky, Nov 30 2021

A372507 a(n) is the smallest number k such that prime(k) is expressible as the sum of (at least two) consecutive primes in n ways.

Original entry on oeis.org

3, 13, 64, 64, 3677, 37096, 259073, 2899722, 88790445, 1554106234, 6711446232, 215580239668

Offset: 1

Ilya Gutkovskiy, May 04 2024

Cf. A000040, A000720, A054859, A067376, A067381, A348791.

a(n) = A000720(A067381(n)).

cp's OEIS Frontend

A065867 Primes which are the sum of a prime number of consecutive primes.

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A348790 a(n) is the smallest number that can be written as the sum of a prime number of consecutive primes in exactly n ways, or -1 if no such number exists.

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A372507 a(n) is the smallest number k such that prime(k) is expressible as the sum of (at least two) consecutive primes in n ways.

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