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

1,1

Comments

There is no term with 15 digits.

Links

Table of n, a(n) for n=1..20.

Index entries for sequences related to final digits of numbers

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

Example

2^36 = 68719476736 which ends in 36.

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 *)

Crossrefs

Cf. A121319, A109405, A206636.

The leading digits are listed in A064540.

Digits read backwards form A133612.

Sequence in context: A138832 A223998 A109405 * A058001 A004329 A089909

Adjacent sequences: A064538 A064539 A064540 * A064542 A064543 A064544

Keyword

base,nonn,nice

Author

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

Status

approved