

A139253


Toothpick primes: primes in the toothpick sequence A139250.


17



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
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OFFSET

1,1


COMMENTS

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


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), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)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


FORMULA

A000040 INTERSECT A139250.


EXAMPLE

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.


MATHEMATICA

toothpicks = With[{terms = 200}, CoefficientList[(x/((1x)(1+2x)))(1 + 2x Product[1 + x^(2^k1) + 2 x^(2^k), {k, 0, Log[2, terms] // Ceiling}]) + O[x]^terms, x]];
Select[toothpicks, PrimeQ] (* JeanFrançois Alcover, Aug 05 2018 *)


CROSSREFS

Intersection of A000040 and A139250.
Cf. A000979, A139251, A139252, A194810.
Sequence in context: A308576 A116362 A090918 * A283588 A283706 A284402
Adjacent sequences: A139250 A139251 A139252 * A139254 A139255 A139256


KEYWORD

nonn


AUTHOR

Omar E. Pol, Apr 24 2008


EXTENSIONS

More terms from Omar E. Pol, Dec 20 2008
Terms beyond 2731 from R. J. Mathar, Jan 21 2010


STATUS

approved



