A064541
Numbers k such that 2^k ends in k.
Original entry on oeis.org
36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736, 8098615075353432948736, 38098615075353432948736
Offset: 1
Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 08 2001
2^36 = 68719476736 which ends in 36.
The leading digits are listed in
A064540.
Digits read backwards form
A133612.
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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 *)
A113627
a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k may have fewer than n digits and can be padded with leading zeros (cf. A121319).
Original entry on oeis.org
14, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 75353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736, 98615075353432948736
Offset: 1
2^14 = 16384 and 14 end with the same single digit 4, thus a(1) = 14.
See
A121319, the main entry for this sequence, for further information.
A121319
a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k must have at least n digits (cf. A113627).
Original entry on oeis.org
14, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 1075353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736
Offset: 1
2^14 = 16384 and 14 end with the same single digit 4, thus a(1) = 14.
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f[n_] := Block[{k = If[n == 1, 2, 10], m = 10^n}, While[ PowerMod[2, k, m] != Mod[k, m], k += 2]; k]; Do[ Print@f@n, {n, 9}] (* Robert G. Wilson v *)
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A121319(n) = { local(k,tn); tn=10^n ; forstep(k=2,1000000000,2, if ( k % tn == (2^k) % tn, return(k) ; ) ; ) ; return(0) ; } { for(n = 1,13, print( A121319(n)) ; ) ; } \\ R. J. Mathar, Aug 27 2006
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