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A321970 Numbers k such that 7^k ends with k. 3
3, 43, 343, 2343, 72343, 172343, 5172343, 65172343, 565172343, 1565172343, 11565172343, 511565172343, 5511565172343, 65511565172343, 265511565172343, 1265511565172343, 31265511565172343, 331265511565172343, 3331265511565172343, 43331265511565172343 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Leftmost digit of a(n) is A133617(n-1) for n <= 30. - Alois P. Heinz, Nov 26 2018

LINKS

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

J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.

EXAMPLE

7^3 = 343, and it ends with 3, so 3 is a term.

MATHEMATICA

a[1] = 3; a[n_] := a[n] = For[ida = IntegerDigits[a[n-1]]; k = 1, True, k++, idk = IntegerDigits[k]; pm = PowerMod[7, an = FromDigits[Join[idk, ida]], 10^IntegerLength[an]]; If[pm == an, Return[an]]]; Array[a, 20] (* after Jean-Fran├žois Alcover in A064541 *)

CROSSREFS

Cf. A133617.

Sequence A064541 is similar, but uses the smallest single-digit prime as a base, unlike this one, which uses the largest single-digit prime as a base.

Sequence in context: A229695 A060559 A197778 * A199349 A197609 A199346

Adjacent sequences:  A321967 A321968 A321969 * A321971 A321972 A321973

KEYWORD

nonn,base

AUTHOR

Ivan Stoykov, Nov 26 2018

STATUS

approved

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Last modified May 25 16:32 EDT 2022. Contains 354071 sequences. (Running on oeis4.)