A391765 a(n) is smallest k such that prime(k) - 1 == 0 (mod n).

1, 2, 4, 3, 5, 4, 10, 7, 8, 5, 9, 6, 16, 10, 11, 7, 27, 8, 43, 13, 14, 9, 15, 21, 26, 16, 29, 10, 17, 11, 64, 25, 19, 27, 20, 12, 35, 43, 22, 13, 23, 14, 40, 24, 42, 15, 61, 25, 45, 26, 27, 16, 28, 29, 67, 30, 50, 17, 127, 18, 73, 64, 31, 44, 32, 19, 57, 33, 34, 20

Offset

1,2

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 1..10000

Formula

A000040(a(n)) - 1 == 0 (mod n).

a(n) = A000720(A034694(n)).

Example

Prime(4) = 7, 7 mod 3 = 1, so a(3) = 4; also 7 mod 6 is 1, so a(6) = 4.

Mathematica

a[1]=1; a[n_]:=Module[{k=1}, While[Mod[Prime[k], n]!=1, k++]; k]; Array[a, 80] (* Stefano Spezia, Dec 19 2025 *)

Prog

(PARI) a(n)= my(p=1, k=1); while(((p=nextprime(p+1))-1)%n, k++); k;

Crossrefs

Cf. A000040, A000720, A034694.

Sequence in context: A328793 A195782 A053049 * A306762 A124938 A198342

Adjacent sequences: A391761 A391762 A391763 * A391766 A391767 A391768

Keyword

nonn

Author

Ruud H.G. van Tol, Dec 19 2025

Status

approved