A022546 -id:A022546 - cp's OEIS frontend

A257377 Numbers n such that n, n+2, n+6, n+12, n+14, n+20, n+24, n+26, n+30, n+36, n+42, n+44, n+50, n+54, n+56, n+62 and n+66 are all prime.

17, 37630850994954402655487, 53947453971035573715707, 174856263959258260646207, 176964638100452596444067, 207068890313310815346497, 247620555224812786876877, 322237784423505559739147

Offset: 1

Tim Johannes Ohrtmann, Apr 21 2015

Tony Forbes k-tuplets

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, this sequence.

A186634 Irregular triangle, read by rows, giving dense patterns of n primes.

Original entry on oeis.org

0, 2, 0, 2, 6, 0, 4, 6, 0, 2, 6, 8, 0, 2, 6, 8, 12, 0, 4, 6, 10, 12, 0, 4, 6, 10, 12, 16, 0, 2, 6, 8, 12, 18, 20, 0, 2, 8, 12, 14, 18, 20, 0, 2, 6, 8, 12, 18, 20, 26, 0, 2, 6, 12, 14, 20, 24, 26, 0, 6, 8, 14, 18, 20, 24, 26, 0, 2, 6, 8, 12, 18, 20, 26, 30, 0, 2, 6, 12, 14, 20, 24, 26, 30, 0, 4, 6, 10, 16, 18, 24, 28, 30, 0, 4, 10, 12, 18, 22, 24, 28, 30, 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 0, 2, 6, 12, 14, 20, 24, 26, 30, 32

Offset: 2

T. D. Noe, Feb 24 2011

The first pattern (0,2) is for twin primes (p,p+2). Row n contains A083409(n) patterns, each one consisting of 0 followed by n-1 terms. In each row the patterns are in lexicographic order.

These numbers (in a slightly different order) appear in Table 1 of the paper by Tony Forbes. Sequence A186702 gives the least prime starting a given pattern.

			The irregular triangle begins:
0, 2
0, 2, 6, 0, 4, 6
0, 2, 6, 8
0, 2, 6, 8, 12, 0, 4, 6, 10, 12
0, 4, 6, 10, 12, 16
0, 2, 6, 8, 12, 18, 20, 0, 2, 8, 12, 14, 18, 20

T. D. Noe, Rows n = 2..20, flattened (from Forbes)
Thomas J. Engelsma, Permissible Patterns
Tony Forbes, Prime clusters and Cunningham chains, Math. Comp. 68 (1999), 1739-1747.
Tony Forbes, Smallest Prime k-tuples
Eric Weisstein's World of Mathematics, Prime Constellation

Cf. A020497, A008407, A186702, and sequences created by these patterns: A001359, A022004, A022005, A007530, A022006, A022007, A022008, A022009, A022010, A022011, A022012, A022013, A022545, A022546, A022547, A022548, A027569, A027570.

cp's OEIS Frontend

A257377 Numbers n such that n, n+2, n+6, n+12, n+14, n+20, n+24, n+26, n+30, n+36, n+42, n+44, n+50, n+54, n+56, n+62 and n+66 are all prime.

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