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

Author

Ivan Stoykov, Nov 26 2018

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• 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.

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.

Programs

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 *)