A060262 a(n) is the smallest k such that prime(k), prime(k+1), ..., prime(k+n-1) all have 10 as a primitive root, but prime(k-1) and prime(k+n) do not.

4, 17, 55, 7, 93, 754, 2611, 31092, 55207, 301252, 955428, 805428, 3651249, 3686621, 5510710, 42337888, 109670084, 590903433, 1010572448

Offset: 1

Author

Jeff Burch, Mar 23 2001

Keywords

• nonn
• more

Comments

A prime p has 10 as a primitive root iff the length of the period of the decimal expansion of 1/p is p-1.

a(21) = 9774718453 and a(23) = 9525468065. - Amiram Eldar, Oct 03 2021

Crossrefs

Cf. A001913, A002371, A060259, A060260, A060261.

Programs

Mathematica

test[p_] := MultiplicativeOrder[10, p]===p-1; For[n=1, n<100, n++, a[n]=0]; v=4; While[True, For[n=1, test[Prime[v+n]], n++, Null]; If[a[n]==0, a[n]=v; Print["a(", n, ") = ", v]]; For[v+=n+1, !test[Prime[v]], v++, Null]]

Extensions

Edited by Dean Hickerson, Jun 17 2002

a(13)-a(19) from Amiram Eldar, Oct 03 2021