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

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, 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, 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

Offset

1,1

Comments

For n > 1, a(n) = A074792(n) is the least solution > 1 of x^n == 1 (mod n). - Robert Israel, Aug 01 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

n*(n + A083502(n)) + 1 = a(n)^n. - R. J. Mathar, Aug 01 2025

Example

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

Maple

A083503 := proc(n)
    local a, b ;
    if n = 1 then
        3 ;
    else
        for b from 2 do
            a := (b^n-1)/n-n ;
            if type( a, 'integer') then
                return  b;
            end if;
        end do:
    end if;
end proc:
seq(A083503(n), n=1..80) ; # R. J. Mathar, Aug 01 2025
# Alternative:
f:= proc(n) local X, S;
  S:= min(map(t -> subs(t, X), {msolve(X^n = 1, n)} minus {{X=1}}));
  if S = infinity then n+1 else S fi
end proc:
f(1):= 3:
map(f, [$1..100]); # Robert Israel, Aug 01 2025

Mathematica

Do[i = 2; While[k = (i^n - 1)/n - n; !IntegerQ[k], i++ ]; Print[i], {n, 2, 81}]

Crossrefs

Cf. A083502, A074792.

Sequence in context: A029882 A163523 A151664 * A342137 A062069 A163375

Adjacent sequences: A083500 A083501 A083502 * A083504 A083505 A083506

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003

Extensions

Edited and extended by Robert G. Wilson v, May 11 2003

Status

approved