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

Author

R. J. Mathar, Jun 29 2020

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A001399, A113653 (isolated semiprimes).

Programs

Maple

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