A377971 Square array of primes p >= 7, read by decreasing antidiagonals. Each row lists, in increasing order, the primes that share the same sum of their neighboring prime gaps.

7, 11, 29, 13, 31, 23, 17, 59, 37, 53, 19, 61, 47, 97, 89, 41, 73, 67, 139, 199, 223, 43, 137, 79, 149, 359, 251, 113, 71, 151, 83, 157, 367, 337, 127, 331, 101, 179, 131, 173, 389, 467, 307, 479, 631, 103, 239, 163, 181, 449, 547, 317, 523, 797, 211, 107, 269, 167, 191, 521, 557, 409, 953, 1087, 293, 1381

Offset

1,1

Comments

First column is subset of A046931, which starts with 3. Here, 3 and 5 are omitted.

The related sum can be denoted Sum_prime_gaps, S = pg_inf + pg_sup.

Links

Table of n, a(n) for n=1..66.

Formula

Sum_prime_gaps_a(n) = S_a(n) = (A002260(n))*2 + 4.

Example

Square array begins:
.
S = pg_inf + pg_sup |
      2*(3..k)      |
-----------------------------------------------------------------------
          6         |   7,  11,  13,  17,  19,  41,  43,  71, 101, ... A098414
          8         |  29,  31,  59,  61,  73, 137, 151, 179, 239, ...
         10         |  23,  37,  47,  67,  79,  83, 131, 163, 167, ...
         12         |  53,  97, 139, 149, 157, 173, 181, 191, 241, ...
         14         |  89, 199, 359, 367, 389, 449, 521, 619, 661, ...
.
31, 59 and 179 are in the same row because their preceding and succeeding prime gaps, (pg_inf, pg_sup), respectively (2,6), (6,2) and (6,2) each equally sum up to 8.
53 and 181 are in the same row because their preceding and succeeding prime gaps, (pg_inf, pg_sup), respectively (6,6) and (2,10) each equally sum up to 12. Here, 53 also happens to be a balanced prime as its corresponding gaps, (6,6), are equal.

Crossrefs

Cf. A000040, A001223, A098414, A002260, A006562.

Sequence in context: A002810 A045736 A158807 * A338929 A067006 A136020

Adjacent sequences: A377968 A377969 A377970 * A377972 A377973 A377974

Keyword

nonn,tabl

Author

Tamas Sandor Nagy, Nov 13 2024

Status

approved