A072967 Least k>n such that the last digit of k^k is the same as the last digit of n^n.

11, 18, 17, 6, 15, 8, 13, 12, 19, 20, 21, 14, 27, 16, 25, 24, 23, 22, 29, 30, 31, 38, 37, 26, 35, 28, 33, 32, 39, 40, 41, 34, 47, 36, 45, 44, 43, 42, 49, 50, 51, 58, 57, 46, 55, 48, 53, 52, 59, 60, 61, 54, 67, 56, 65, 64, 63, 62, 69, 70, 71, 78, 77, 66, 75, 68, 73, 72, 79, 80

Offset

1,1

Links

Zhuorui He, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

a(n) = n + A072968(n) where A072968(n) is a periodic sequence with period (10, 16, 14, 2, 10, 2, 6, 4, 10, 10, 10, 2, 14, 2, 10, 8, 6, 4, 10, 10) of length 20. [corrected by Zhuorui He, Jun 13 2026]

a(n+20) = a(n) + 20. - Zhuorui He, Jun 13 2026

Mathematica

lkld[n_]:=Module[{ldn=Mod[n^n, 10], k=n+2}, While[Mod[k^k, 10]!=ldn, k=k+2]; k]; Array[lkld, 70] (* Harvey P. Dale, Feb 15 2015 *)

Prog

(PARI) a(n)=if(n<0, 0, s=n+1; while(abs(s^s%10-n^n%10)>0, s++); s)

Crossrefs

Cf. A072968.

Sequence in context: A257169 A162555 A059141 * A232658 A300062 A309489

Adjacent sequences: A072964 A072965 A072966 * A072968 A072969 A072970

Keyword

base,easy,nonn

Author

Benoit Cloitre, Aug 13 2002

Status

approved