A321970 Numbers k such that 7^k ends with k.

3, 43, 343, 2343, 72343, 172343, 5172343, 65172343, 565172343, 1565172343, 11565172343, 511565172343, 5511565172343, 65511565172343, 265511565172343, 1265511565172343, 31265511565172343, 331265511565172343, 3331265511565172343, 43331265511565172343

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-François 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