cp's OEIS Frontend

A083503 Basis of the n-th power arising in A083502.

%I A083503 #24 Aug 04 2025 02:26:05
%S A083503 3,3,4,3,6,5,8,3,4,9,12,5,14,13,16,3,18,5,20,3,4,21,24,5,6,25,4,13,30,
%T A083503 11,32,3,34,33,36,5,38,37,16,3,42,5,44,21,16,45,48,5,8,9,52,5,54,5,16,
%U A083503 13,7,57,60,7,62,61,4,3,66,23,68,13,70,29,72,5,74,73,16,37,78,17,80,3,4
%N A083503 Basis of the n-th power arising in A083502.
%C A083503 For n > 1, a(n) = A074792(n) is the least solution > 1 of x^n == 1 (mod n). - _Robert Israel_, Aug 01 2025
%H A083503 Robert Israel, <a href="/A083503/b083503.txt">Table of n, a(n) for n = 1..10000</a>
%F A083503 n*(n + A083502(n)) + 1 = a(n)^n. - _R. J. Mathar_, Aug 01 2025
%e A083503 2*(2+2)+1=3^2; 3*(3+18)+1=4^3; 4*(4+16)+1=3^4; 5*(5+1550)+1=6^5; 6*(6+2598)+1=5^6; 7*(7+299586)+1=8^7; 8*(8+812)+1=3^8; 9*(9+29118)+1=4^9; 10*(10+348678430)+1=9^10. - _R. J. Mathar_, Aug 01 2025
%p A083503 A083503 := proc(n)
%p A083503     local a,b ;
%p A083503     if n = 1 then
%p A083503         3 ;
%p A083503     else
%p A083503         for b from 2 do
%p A083503             a := (b^n-1)/n-n ;
%p A083503             if type( a,'integer') then
%p A083503                 return  b;
%p A083503             end if;
%p A083503         end do:
%p A083503     end if;
%p A083503 end proc:
%p A083503 seq(A083503(n),n=1..80) ; # _R. J. Mathar_, Aug 01 2025
%p A083503 # alternative:
%p A083503 f:= proc(n) local X,S;
%p A083503   S:= min(map(t -> subs(t,X), {msolve(X^n = 1, n)} minus {{X=1}}));
%p A083503   if S = infinity then n+1 else S fi
%p A083503 end proc:
%p A083503 f(1):= 3:
%p A083503 map(f, [$1..100]); # _Robert Israel_, Aug 01 2025
%t A083503 Do[i = 2; While[k = (i^n - 1)/n - n; !IntegerQ[k], i++ ]; Print[i], {n, 2, 81}]
%Y A083503 Cf. A083502, A074792.
%K A083503 nonn
%O A083503 1,1
%A A083503 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003
%E A083503 Edited and extended by _Robert G. Wilson v_, May 11 2003