A358348 - OEIS

%I #48 Mar 29 2023 06:37:36

%S 1,4,7,9,10,13,16,17,18,19,22,25,27,28,31,34,35,36,37,40,43,45,46,49,

%T 52,53,54,55,58,61,63,64,67,70,71,72,73,76,79,81,82,85,88,89,90,91,94,

%U 97,99,100,103,106,107,108,109,112,115,117,118,121,124,125,126

%N Numbers k such that k == k^k (mod 9).

%C Each multiple of 9 is in the sequence. Additionally, the squares are also present.

%D M. Fujiwara and Y. Ogawa, Introduction to Truly Beautiful Mathematics. Tokyo: Chikuma Shobo, 2005.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,-1).

%F G.f.: x*(x+1)*(x^7+3*x^5+x^3+x^2+2*x+1)/((1-x)^2*(1+x^3+x^6)*(1+x+x^2)). - _Alois P. Heinz_, Feb 08 2023

%F a(n) = 2*(n+1) - b(n) where b(n>=0) = 2,3,2,1,1,2,1,0,1,2,3,2,... has period 9. - _Kevin Ryde_, Mar 26 2023

%e 4 is a term since 4^4 = 256 == 4 (mod 9).

%p A358348 := proc(n)

%p     2*(n+1)-op(modp(n,9)+1,[2,3,2,1,1,2,1,0,1]) ;

%p end proc:

%p seq(A358348(n),n=1..50) ; # _R. J. Mathar_, Mar 29 2023

%t Select[Range[130], MemberQ[{0, 1, 4, 7, 9, 10, 13, 16, 17}, Mod[#, 18]] &] (* _Amiram Eldar_, Nov 12 2022 *)

%o (PARI) isok(k) = k == Mod(k,9)^k; \\ _Michel Marcus_, Nov 22 2022

%o (Python)

%o def A358348(n):

%o     return ((0, 1, 4, 7, 9, 10, 13, 16, 17)[m := n % 9]

%o          + (n - m << 1))  # _Chai Wah Wu_, Feb 09 2023

%Y Cf. A007953, A010888, A082576, A189510.

%K nonn,base,easy

%O 1,2

%A _Ivan Stoykov_, Nov 11 2022