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 A072968 Least k>0 such that the last digit of (n+k)^(n+k) is the same as the last digit of n^n. 0
 10, 16, 14, 2, 10, 2, 6, 4, 10, 10, 10, 2, 14, 2, 10, 8, 6, 4, 10, 10, 10, 16, 14, 2, 10, 2, 6, 4, 10, 10, 10, 2, 14, 2, 10, 8, 6, 4, 10, 10, 10, 16, 14, 2, 10, 2, 6, 4, 10, 10, 10, 2, 14, 2, 10, 8, 6, 4, 10, 10, 10, 16, 14, 2, 10, 2, 6, 4, 10, 10, 10, 2, 14, 2, 10, 8, 6, 4, 10, 10, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..81. Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1). FORMULA a(n) is periodic with period (10, 16, 14, 2, 10, 2, 6, 4, 10, 10, 10, 2, 14, 2, 10, 8, 6, 4, 10, 10, 10) of length 20 MATHEMATICA ld[n_]:=Module[{ldn=Mod[n^n, 10], k=1}, While[Mod[(n+k)^(n+k), 10] != ldn, k++]; k]; Array[ld, 90] (* Harvey P. Dale, Sep 07 2012 *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {10, 16, 14, 2, 10, 2, 6, 4, 10, 10, 10, 2, 14, 2, 10, 8, 6, 4, 10, 10}, 81] (* Ray Chandler, Aug 26 2015 *) PROG (PARI) a(n)=if(n<0, 0, s=1; while(abs((n+s)^(n+s)%10-n^n%10)>0, s++); s) (Python) def a(n): k, target = 1, pow(n, n, 10) while pow(n+k, n+k, 10) != target: k += 1 return k print([a(n) for n in range(1, 82)]) # Michael S. Branicky, Oct 16 2021 CROSSREFS Sequence in context: A175335 A167788 A341012 * A072138 A109891 A104869 Adjacent sequences: A072965 A072966 A072967 * A072969 A072970 A072971 KEYWORD base,easy,nonn AUTHOR Benoit Cloitre, Aug 13 2002 STATUS approved

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Last modified June 8 07:13 EDT 2023. Contains 363157 sequences. (Running on oeis4.)