A335916 Isolated primes in the hexagonal spiral of the nonnegative integers.

83, 97, 107, 127, 157, 167, 193, 233, 239, 257, 263, 269, 281, 293, 307, 311, 313, 317, 347, 349, 359, 367, 383, 401, 409, 419, 431, 439, 457, 467, 487, 499, 503, 521, 523, 563, 569, 577, 593, 599, 601, 607, 617, 653, 661, 677, 683, 691, 719, 743, 757, 769, 773, 797, 811, 821, 839, 853

Offset

1,1

Comments

Plotting the integers on a hexagonal grid as in A001399 associates each n>=0 with six different neighbors to the E, NE, NW, W, SE and SW. If n is prime and all 6 neighbors are composite, n is in the sequence.

Links

Table of n, a(n) for n=1..58.

Example

The six neighbors of the prime 7 are 1, 6, 8, 18, 19, 20; 19 is also prime, so 7 is not in the sequence.
The six neighbors of the prime 83 are 54, 55, 82, 84, 117 and 118 which are all composite, so 83 is in the sequence.

Maple

# replace isA001358 by isprime in the coding for A113653, and isA113653 by isA335916.

Crossrefs

Cf. A001399, A113653 (isolated semiprimes).

Sequence in context: A045714 A090156 A220121 * A158719 A160028 A115258

Adjacent sequences: A335913 A335914 A335915 * A335917 A335918 A335919

Keyword

nonn

Author

R. J. Mathar, Jun 29 2020

Status

approved