A055737 Number of prime triples < 10^n, where a prime triple means 3 successive primes of the form {p, p+2, p+4} or {p, p+4, p+6}.

0, 8, 30, 112, 507, 2837, 17220, 111156, 759256, 5425573, 40174725, 305689269, 2379622234, 18887841658

Offset: 1

Author

Robert G. Wilson v, Jun 09 2000

Keywords

• more
• nonn

Comments

For this sequence all three members of the triple must be below the 10^n bound. - Sean A. Irvine, Apr 04 2022

References

• J. Recreational Math., vol. 23, No. 2, 1991, p. 97.

Links

• Index entries for sequences related to numbers of primes in various ranges

Crossrefs

Cf. A055738, A006880, A007529, A098415.

Programs

Mathematica

x=168; a=Table[ Prime[ n ], {n, 1, x} ] c=0; Do[ If[ a[[ n ]]+6==a[ [ n+2 ] ], c++ ], {n, 1, x-2} ]; c # the values of x to use are given by A006880

Extensions

a(7)-a(9) from Jud McCranie, Oct 07 2000

a(10)-a(12) from Martin Raab, Oct 04 2006

a(13)-a(14) from Charles R Greathouse IV, Feb 09 2022