A139253 Toothpick primes: primes in the toothpick sequence A139250.

3, 7, 11, 23, 43, 47, 67, 79, 223, 251, 283, 347, 383, 571, 683, 719, 859, 1163, 1279, 1319, 1607, 1667, 1759, 1871, 2011, 2731, 2767, 2843, 2879, 3919, 4523, 4783, 4799, 4903, 5051, 6343, 6607, 7823, 8971, 9643, 11003, 11071, 11483, 11519, 12251, 12907

Offset: 1

Author

Omar E. Pol, Apr 24 2008

Keywords

• nonn

Comments

All Wagstaff primes A000979 are members of this sequence. - Omar E. Pol, Mar 12 2012

Examples

			a(25) = 2011 because 2011 is the number of toothpicks after 60 stages in the toothpick structure of A139250 and it is also a prime number A000040.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..181
• David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.], arXiv:1004.3036
• Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 2011
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

Intersection of A000040 and A139250.

Cf. A000979, A139251, A139252, A194810.

Programs

Mathematica

toothpicks = With[{terms = 200}, CoefficientList[(x/((1-x)(1+2x)))(1 + 2x Product[1 + x^(2^k-1) + 2 x^(2^k), {k, 0, Log[2, terms] // Ceiling}]) + O[x]^terms, x]];
Select[toothpicks, PrimeQ] (* Jean-François Alcover, Aug 05 2018 *)

Formula

A000040 INTERSECT A139250.

Extensions

More terms from Omar E. Pol, Dec 20 2008

Terms beyond 2731 from R. J. Mathar, Jan 21 2010