A074250 Smallest p>1 for which n^p ends in n, or -1 if no such p exists. The smallest p for which n is a p-morphic number.

2, 5, 5, 3, 2, 2, 5, 5, 3, -1, 11, 21, 21, -1, -1, 6, 21, -1, 11, -1, 6, -1, 21, 3, 2, -1, 21, 21, 11, -1, 11, 5, 21, -1, -1, 6, 21, -1, 11, -1, 6, -1, 5, 11, -1, -1, 21, 21, 3, -1, 3, 21, 21, -1, -1, 6, 5, -1, 11, -1, 6, -1, 21, 11, -1, -1, 21, 5, 11, -1, 11, 21, 21, -1, 3, 2, 21, -1, 11, -1, 6, -1, 21, 11, -1, -1, 21, 21, 11, -1, 11, 21, 5, -1

Offset: 1

Author

Zak Seidov, Sep 20 2002

Keywords

• sign
• base

Comments

For n < 201, 83 numbers cannot be p-morphic numbers, while 116 numbers can be p-morphic number with smallest p varying from, e.g., p(5)=3 to p(103)=101. The smallest power p>1 for which n^p has n somewhere (not necessarily at the end!) in its decimal representation is A045537. If positive, the values of p in A045537 are smaller than p in this sequence.

Examples

			a(12) = 21 because 12^21 is the smallest power (>1) of 12 that ends in 12 (that, is 12 is a 21-morphic number); a(14) = -1 because there is no power (>1) of 14 that ends in 14 (that is, 14 cannot be any p-morphic number).
		

Links

• Index entries for sequences related to automorphic numbers

Crossrefs

Cf. A045537.

Programs

Mathematica

SelectFirst[Range[2, 120], Function[k, Mod[#^k, 10^IntegerLength@ #] == #]] & /@ Range@ 200 /. n_ /; MissingQ@ n -> -1 (* Michael De Vlieger, Dec 02 2015, Version 10 *)