A194810 Indices k such that A139250(k) = A000979(n).

2, 4, 8, 32, 64, 256, 512, 2048, 32768, 2097152, 1073741824, 549755813888, 1125899906842624, 9223372036854775808, 9671406556917033397649408, 39614081257132168796771975168, 633825300114114700748351602688

Offset

1,1

Comments

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).

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).

Links

Table of n, a(n) for n=1..17.

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.]

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, arXiv:1004.3036 [math.CO], 2010.

David Applegate, The movie version

C. Caldwell's The Top Twenty, Wagstaff.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Wikipedia, Wagstaff prime

Formula

a(n) = 2^A127936(n) = 2^(floor(A000978(n)/2)) = 2^(ceiling(log_4(A000979(n)))).

A139250(2^n) = A007583(n), n >= 0.

A139250(a(n)) = A000979(n).

Example

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.

Mathematica

2^Reap[Do[If[PrimeQ[1+Sum[2^(2n-1), {n, m}]], Sow[m]], {m, 100}]][[2, 1]] (* Jean-François Alcover, Oct 06 2018 *)

Crossrefs

Cf. A000978, A000979, A007583, A001045, A127936, A127958, A127962, A127965, A139250, A139253.

Sequence in context: A053147 A128055 A061285 * A271216 A102000 A372256

Adjacent sequences: A194807 A194808 A194809 * A194811 A194812 A194813

Keyword

nonn

Author

Omar E. Pol, Oct 23 2011

Extensions

More terms from Omar E. Pol, Mar 14 2012

Status

approved