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 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 (list; graph; refs; listen; history; text; internal format)
 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), 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 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/((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 *) CROSSREFS Intersection of A000040 and A139250. Cf. A000979, A139251, A139252, A194810. Sequence in context: A106935 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

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)