A379677 Numbers k for which 10k+1, 10k+3, 10k+7, 10k+9, 10k+31, 10k+33, 10k+37, and 10k+39 are primes.

100630, 259495, 391921, 960055, 1053106, 10881631, 13144570, 15237073, 15713164, 17902876, 21195025, 25535221, 26758786, 55745863, 68512435, 72449137, 82135765, 87141136, 103026208, 110310436, 128216002, 138120127, 142769863, 143237995, 144399400, 159672133, 194876008

Offset: 1

Author

Mike Speciner, Dec 29 2024

Keywords

• nonn

Comments

k is a term if k and k+3 are both in A007811.

Examples

			a(1) = 100630 since 1006301, 1006303, 1006307, 1006309, 1006331, 1006333, 1006337, and 1006339 are all prime and there are no smaller minimally close prime decades.
		

Crossrefs

Cf. A007811, A059925.

Programs

Python

from itertools import count
from sympy import isprime
def generate_a() :
  for k in count() :
    for j in (1,3,7,9,31,33,37,39) :
      if not isprime(10*k+j) : break
    else:
      yield k

Formula

From Hugo Pfoertner, Dec 29 2024: (Start)

a(n) = (A059925(n) - 1)/10.

a(n) == 19 (mod 21). (End)

Extensions

More terms from Hugo Pfoertner, Dec 29 2024