A372248 -id:A372248 - cp's OEIS frontend

A372085 Primes starting a sequence of 6 consecutive primes with gaps 2, 4, 8, 16, 32.

6824897, 10132607, 12674657, 13699457, 14148047, 27353237, 43918997, 44152307, 50608007, 53944337, 60426257, 60825827, 61325057, 68721047, 68933717, 72069707, 78577817, 82108127, 82334297, 87020177, 88226777, 97013927, 102043757, 106053917, 122271557, 140859707, 146049047, 161788787, 162036227

Offset: 1

Zak Seidov and Robert Israel, Apr 17 2024

nonn

First differs from A079015 at a(25) = 122271557.

All terms == 7 (mod 10).

			a(3) = 12674657 is a term because 12674657 is prime and the next five primes are 12674657 + 2 = 12674659, 12674659 + 4 = 12674663, 12674663 + 8 = 12674671, 12674671 + 16 = 12674687 and 12674687 + 32 = 12674719.

Robert Israel, Table of n, a(n) for n = 1..1000
Index entries for primes, gaps between

Cf. A079015, A372248 (gaps 2,4,8,16).

p:= 2: state:= 1: count:= 0: Res:= NULL:
while count < 100 do
  q:= nextprime(p);
  if q - p = 2^state then
     state:= state+1;
     if state = 6 then
       count:= count+1; Res:= Res,q-62;
     fi;
  else state:= 1
  fi;
  p:= q;
od:
Res;

A372247 Lowest prime p in a ladder of 4 consecutive primes p, p+2, p+6, p+14.

Original entry on oeis.org

1997, 2237, 2267, 2657, 6197, 6827, 8087, 17027, 17387, 19427, 21017, 21377, 22277, 22637, 23057, 24107, 29567, 37307, 43397, 43787, 53087, 55337, 56807, 58907, 62297, 65537, 65837, 78887, 81017, 82007, 82217, 89597, 90017, 91367, 93887, 95087, 97547, 105527, 108287, 110567, 112247, 113357

Offset: 1

R. J. Mathar, Apr 24 2024

nonn

			2267, 2269, 2273 and 2281 are consecutive primes with gaps of 2, 4 and 8, so 2267 is in the sequence.

Subsequence of A022004. A372248 is a subsequence.

First /@ Parallelize[
  Select[Table[NextPrime[Prime@i, Range@4], {i, 10^5}],
   Differences@# == {2, 4, 8} &]] (* Mikk Heidemaa, Apr 25 2024 *)

cp's OEIS Frontend

A372085 Primes starting a sequence of 6 consecutive primes with gaps 2, 4, 8, 16, 32.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple