

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 pmorphic number.


1



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
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OFFSET

1,1


COMMENTS

For n < 201, 83 numbers cannot be pmorphic numbers, while 116 numbers can be pmorphic 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



EXAMPLE

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



KEYWORD

sign,base


AUTHOR



STATUS

approved



