This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A194810 #67 Apr 03 2023 10:36:12
%S A194810 2,4,8,32,64,256,512,2048,32768,2097152,1073741824,549755813888,
%T A194810 1125899906842624,9223372036854775808,9671406556917033397649408,
%U A194810 39614081257132168796771975168,633825300114114700748351602688
%N A194810 Indices k such that A139250(k) = A000979(n).
%C A194810 Indices k such that the number of toothpicks in the toothpick structure of A139250 after k-th stage equals the n-th Wagstaff prime A000979. All terms of this sequence are powers of 2 (see formulas).
%C A194810 For a picture of the n-th Wagstaff prime as a toothpick structure see the Applegate link "A139250: the movie version", then enter N = a(n) and click "Update", for N = a(n) <= 32768 (due to the resolution of the movie).
%H A194810 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]
%H A194810 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="http://arxiv.org/abs/1004.3036">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, arXiv:1004.3036 [math.CO], 2010.
%H A194810 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H A194810 C. Caldwell's The Top Twenty, <a href="https://t5k.org/top20/page.php?id=67">Wagstaff</a>.
%H A194810 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H A194810 Wikipedia, <a href="http://en.wikipedia.org/wiki/Wagstaff_prime">Wagstaff prime</a>
%F A194810 a(n) = 2^A127936(n) = 2^(floor(A000978(n)/2)) = 2^(ceiling(log_4(A000979(n)))).
%F A194810 A139250(2^n) = A007583(n), n >= 0.
%F A194810 A139250(a(n)) = A000979(n).
%e A194810 For n = 5 we have that a(5) = 64, then we can see that the number of toothpicks in the toothpick structure of A139250 after 64 stages is 2731 which coincides with the fifth Wagstaff prime, so we can write A139250(64) = A000979(5) = 2731. See the illustration in the Applegate-Pol-Sloane paper, figure 3: T(64) = 2731 toothpicks.
%t A194810 2^Reap[Do[If[PrimeQ[1+Sum[2^(2n-1), {n, m}]], Sow[m]], {m, 100}]][[2, 1]] (* _Jean-François Alcover_, Oct 06 2018 *)
%Y A194810 Cf. A000978, A000979, A007583, A001045, A127936, A127958, A127962, A127965, A139250, A139253.
%K A194810 nonn
%O A194810 1,1
%A A194810 _Omar E. Pol_, Oct 23 2011
%E A194810 More terms from _Omar E. Pol_, Mar 14 2012