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

1,1

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.

Links

Table of n, a(n) for n=1..94.

Index entries for sequences related to automorphic numbers

Example

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).

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 *)

Crossrefs

Cf. A045537.

Sequence in context: A153354 A153821 A153879 * A161013 A115522 A362138

Adjacent sequences: A074247 A074248 A074249 * A074251 A074252 A074253

Keyword

sign,base

Author

Zak Seidov, Sep 20 2002

Status

approved