A172294 Sequence of the "Natural Jewels": a natural jewel is a number that is totally enclosed by prime numbers in a version of Ulam Spiral.

12, 42, 1152, 1452, 1950, 3672, 5520, 6660, 8232, 10890, 13218, 15288, 15360, 16062, 18042, 20898, 21018, 23562, 23628, 25998, 27918, 32190, 37812, 42018, 42462, 48858, 55818, 57192, 80832, 80910, 83232, 83340, 91368, 97848, 98640

Offset

1,1

Comments

There is no formula to calculate these numbers. If the sequence is infinite, then there are infinitely many primes p such that p + 2 is also prime (twin prime conjecture).

Links

Table of n, a(n) for n=1..35.

Emilio Apricena, Illustration

Example

11-(top)->12, 13-(left)->12, 29-(right)->12, 31-(bottom)->12.

Crossrefs

Cf. A156859.

Sequence in context: A334277 A122973 A074356 * A238225 A088826 A125221

Adjacent sequences: A172291 A172292 A172293 * A172295 A172296 A172297

Keyword

nonn

Author

Emilio Apricena (emilioapricena(AT)yahoo.it), Jan 30 2010

Extensions

Corrected and extended by Emilio Apricena (emilioapricena(AT)yahoo.it), May 15 2010

Status

approved