A225795 Smallest k > 1 such that k^n has k as its middle digits, or 0 if no such k exists.

2, 50, 50, 60, 70, 6, 2, 7600, 47, 5, 4, 93, 6, 34, 5, 9600, 71, 4, 74, 320, 3, 372, 13, 846, 32, 9600, 339, 9765, 202, 3, 69, 6, 9900, 13, 8586, 9600, 4, 46, 3, 4, 446, 3, 9900, 4, 1256, 614, 819, 3365, 8, 36400, 76, 647, 35, 39548, 9900, 4740

Offset: 1

Author

Michel Lagneau, Jul 27 2013

Keywords

• nonn
• base

Comments

Is a(88) the first 0? If a(88) is nonzero, it is greater than 2 * 10^8. - T. D. Noe, Jul 29 2013

Examples

			a(6) = 6 because 6^6 = 46656 has 6 as its middle digit.
		

Crossrefs

Cf. A062118.

Programs

Mathematica

Table[k = 2; While[c0 = IntegerDigits[k]; c1 = IntegerDigits[k^n]; len0 = Length[c0]; len1 = Length[c1];  f = (len1 - len0)/2; ! (OddQ[len0] == OddQ[len1] && c0 == Take[c1, {f + 1, f + len0}]), k++]; k, {n, 56}] (* T. D. Noe, Jul 29 2013 *)

Extensions

Corrected by T. D. Noe, Jul 29 2013