A228102 -id:A228102 - cp's OEIS frontend

A344580 Numbers k such that A101203(k) is prime.

4, 5, 6, 7, 8, 15, 18, 19, 26, 33, 44, 50, 64, 69, 74, 115, 138, 139, 150, 151, 161, 170, 208, 213, 218, 232, 233, 237, 246, 258, 275, 289, 290, 303, 309, 310, 311, 333, 334, 340, 352, 353, 360, 369, 376, 405, 412, 441, 483, 489, 495, 502, 503, 507, 514, 529, 610, 615, 633, 638, 645, 648, 658

Offset: 1

J. M. Bergot and Robert Israel, May 23 2021

nonn

Numbers k such that the sum of nonprimes <= k is prime.

If p is prime then p is a member if and only if p-1 is a member.

			a(3) = 6 is a member because A101203(6) = 1+4+6 = 11 is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A101203, A228102.

s:= proc(n) option remember; if isprime(n) then procname(n-1) else procname(n-1)+ n fi end proc:
s(1):= 1:
select(n -> isprime(s(n)), [$1..1000]);

A228357 Numbers n such that sum of all primes <=n is not prime.

Original entry on oeis.org

1, 5, 6, 11, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 41, 42, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85

Offset: 1

Vincenzo Librandi, Aug 21 2013

			6 is in the sequence since 2+3+5=10 is not prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A034387, A228102.

[n: n in [1..120] | not IsPrime(s) where s is &+PrimesUpTo(n)];

t = {}; s = 0; Do[If [PrimeQ[n], s+ = n]; If[!PrimeQ[s], AppendTo[t, n]], {n, 120}]; t
Position[Accumulate[Table[If[PrimeQ[n],n,0],{n,100}]],?(!PrimeQ[ #]&)]// Flatten//Rest (* _Harvey P. Dale, Jul 02 2018 *)

A344581 Numbers k such that A034387(k) and A101203(k) are both prime.

Original entry on oeis.org

4, 7, 8, 15, 44, 311, 503, 507, 744, 843, 851, 955, 1164, 1256, 1287, 1307, 1312, 2163, 2171, 2244, 2247, 2368, 2412, 3143, 3160, 3872, 3875, 3952, 4584, 5088, 5236, 5355, 5364, 5380, 6211, 6303, 6307, 6587, 7243, 7244, 7436, 7439, 7860, 8220, 8268, 9167, 9283, 9515, 9519, 9632, 9692, 9915, 9919

Offset: 1

J. M. Bergot and Robert Israel, May 24 2021

nonn

Numbers k such that the sums of primes <= k and of nonprimes <= k are both prime (not necessarily distinct).

All terms == 0 or 3 (mod 4).

			a(3) = 8 is a term because A034387(8) = 2+3+5+7 = 17 and A101203(8) = 1+4+6+8 = 19 are prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A034387, A101203. Intersection of A228102 and A344580.

sp:= proc(n) option remember; if isprime(n) then procname(n-1)+[0,n] else procname(n-1)+[n,0] fi end proc:
sp(1):= [1,0]:
filter:= proc(n) andmap(isprime, sp(n)) end proc:
select(filter, [$1..10000]);

cp's OEIS Frontend

A344580 Numbers k such that A101203(k) is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

A228357 Numbers n such that sum of all primes <=n is not prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A344581 Numbers k such that A034387(k) and A101203(k) are both prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple