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A187063 Numbers of the form (4^k - 1)/3 whose greatest prime divisor is of the form 2^q - 1 or 2^q + 1. 1
5, 21, 85, 341, 5461, 21845, 22369621, 89478485, 1431655765, 5726623061, 91625968981, 1501199875790165, 1537228672809129301, 98382635059784275285, 1690200800304305868662270940501, 1772303994379887830538409413707126101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The binary expansion of (4^k-1)/3 has no consecutive equal binary digits.

The corresponding values of k are 2, 3, 4, 5, 7, 8, 13, 14, 16, 17, 19, 26, 31, 34, 51, 61, 62, 89, 107, 122, 127, 178, 214, 254, 521, ... - Amiram Eldar, Mar 02 2020

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..25

EXAMPLE

(4^6-1)/3 = 1365 = 3 * 5 * 7 * 13 is not in the sequence because  13 is not of the form 2^q +/- 1 ;

(4^16-1)/3 = 1431655765 = 5 * 17 * 257 * 65537 and 65537 = 2^16 + 1.

MAPLE

with(numtheory):

a:= proc(n) option remember; local k, t, d, h;

      for k from 1+ `if`(n=1, 0, ilog[4](a(n-1)*3+1))

      do t:= (4^k-1)/3;

         d:= max(factorset(t)[]);

         for h in [d+1, d-1] do

            if 2^ilog[2](h)=h then RETURN(t) fi

         od

      od

    end:

seq(a(n), n=1..17);  # Alois P. Heinz, Mar 04 2011

MATHEMATICA

okQ[n_] := Module[{p = FactorInteger[n][[-1, 1]]}, IntegerQ[Log[2, p + 1]] || IntegerQ[Log[2, p - 1]]]; t = Table[(4^n-1)/3, {n, 2, 50}]; Select[t, okQ] (* T. D. Noe, Mar 04 2011 *)

CROSSREFS

Cf. A002450 ((4^n-1)/3), A274906.

Sequence in context: A028948 A084241 A002450 * A026855 A272832 A273489

Adjacent sequences:  A187060 A187061 A187062 * A187064 A187065 A187066

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 03 2011

STATUS

approved

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)