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

Author

Zak Seidov and Robert Israel, Apr 17 2024

Keywords

• nonn

Comments

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

All terms == 7 (mod 10).

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Maple

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;