User talk:M. F. Hasler/drafts/A008471

Decades containing exactly 3 primes

4, 7, 13, 22, 31, 43, 46, 61, 64, 85, 88, 103, 106, 109, 130, 142, 145, 160, 166, 169, 178, 199, 238, 268, 271, 316, 367, 376, 391, 400, 409, 415, 421, 451, 472, 478, 493, 523, 541, 544, 547, 550, 574, 586, 670, 682, 712, 721, 745, 748, 754, 775, 787, 808, 823, 829, 862, 883, 886, 904, 934, 946, 985, ...

Comment

• A number K = a(n) is in the sequence iff there are exactly 3 primes in between 10 K and 10 K + 10.
• This is a subsequence of A171251, which lists decades that may contain 3 or 4 primes.
• If the sequence contains K-3 or K+3 along with K, then K is part of a "run of consecutive decadal triplets". The run lengths of these are listed in A171256.
• As explained in A171251, all terms are of the form 3k+1. The sequence of k-values is

1, 2, 4, 7, 10, 14, 15, 20, 21, 28, 29, 34, 35, 36, 43, 47, 48, 53, 55, 56, 59, 66, 79, 89, 90, 105, 122, 125, 130, 133, 136, 138, 140, 150, 157, 159, 164, 174, 180, 181, 182, 183, 191, 195, 223, 227, 237, 240, 248, 249, 251, 258, 262, 269, 274, 276, 287, 294, 295, 301, 311, 315, 328, ...

Formula

a(n) = [ A171255(n)) / 10 ]

Crossrefs

Was already in OEIS as A008471 when I originally (during 2010 downtime due to move to new server) planned to submit it as A171254.

• User talk:M. F. Hasler/drafts/A171251 Decades with prime triplets. TO DO : fix reference!
• ../A171252 Least member of decadal prime triplets
• ../A171253 Largest member of decadal prime triplet
• A008471: Exactly 3 out of 10m+1, 10m+3, 10m+7, 10m+9 are primes. My notes: ../A008471 - originally planned to be A171254 / ../A171254 / "Decades containing exactly 3 primes"
• ../A171255 Least prime in a decade containing exactly 3 primes.
• A238716: Run lengths of decadal prime triplets. Notes: ../A238716; initially planned to be A171256 : ../A171256
• A238715: Least prime of a run of 3 or more consecutive decadal prime triplets. Notes: ../A238715; initially planned to be A171257 : ../A171257

Author

— M. F. Hasler 20:55, 3 January 2010 (UTC)