A086003 Primes which remain prime after one and after two applications of the rotate-and-add operation of A086002.

271, 281, 10853, 10903, 10939, 12917, 12919, 16603, 16673, 16823, 16843, 18671, 18911, 18913, 20929, 22817, 22907, 24907, 26813, 26833, 26903, 26947, 28661, 28901, 28921, 30809, 30829, 32831, 32917, 32941, 34939, 36653, 36913, 38651

Offset: 1

Author

Chuck Seggelin, Jul 07 2003

Keywords

• base
• nonn

Comments

The rotate operation of nonnegative integers is defined in A086002, which lists the primes that remain prime after one application of the compound rotate-and-add operation. The sequence here lists those primes p which in addition remain prime after applying this transformation twice, that is, those elements of A086002 such that the image of the rotate-and-add operation is again in A086002.

Examples

			a(6)=12917 because (i) 12917 is prime. (ii) rotate(12917) = 17912 and 12917+17912=30829 which is also prime. (iii) rotate(30829) = 29830 and 30829+29830=60659 which is also prime.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086002, A086004.

Formula

{p in A086002: p+rot(p) in A086002}.

Extensions

Edited by R. J. Mathar, May 27 2009