A064541 Numbers k such that 2^k ends in k.

36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736, 8098615075353432948736, 38098615075353432948736

Offset: 1

Author

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 08 2001

Keywords

• base
• nonn
• nice

Comments

There is no term with 15 digits.

Examples

			2^36 = 68719476736 which ends in 36.
		

Links

• Index entries for sequences related to final digits of numbers

Crossrefs

Cf. A121319, A109405, A206636.

The leading digits are listed in A064540.

Digits read backwards form A133612.

Programs

Mathematica

a[1] = 36; a[n_] := a[n] = For[ida = IntegerDigits[a[n-1]]; k = 1, True, k++, idk = IntegerDigits[k]; pm = PowerMod[2, an = FromDigits[Join[idk, ida]], 10^IntegerLength[an]]; If[pm == an, Return[an]]]; Array[a, 20] (* Jean-François Alcover, Feb 15 2018 *)

Formula

a(n+1) is a suffix of 2^a(n) formed by a nonzero digit followed by a number of zeros and a(n). E.g., a(13)=75353432948736 and 2^a(13) ends with ...15075353432948736, hence a(14)=5075353432948736. - Max Alekseyev, Apr 18 2007

Can be obtained from A109405 by removing all repeats. - Max Alekseyev, May 11 2007