A227969 Powers of primes other than 2 and 5 in order by cycle length of reciprocal in decimal.

3, 9, 11, 27, 37, 101, 41, 271, 7, 13, 239, 4649, 73, 137, 81, 333667, 9091, 21649, 513239, 9901, 53, 79, 265371653, 909091, 31, 2906161, 17, 5882353, 2071723, 5363222357, 19, 52579, 1111111111111111111, 3541, 27961, 43, 1933, 10838689, 23, 121, 4093, 8779, 11111111111111111111111

Offset: 1

Author

J. Lowell, Aug 01 2013

Keywords

• nonn
• tabf
• base

Examples

			3 and 9 qualify for the first 2 terms because both of them have a reciprocal cycle of 1. Then 11 has a reciprocal cycle of 2; then 27 and 37 have 3; then 101 has 4; then 41 and 271 have 5. Table begins:
3, 9;
11;
27, 37;
101;
41, 271;
7, 13;
239, 4649;
73, 137;
81, 333667;
9091;
21649, 513239;
9901;
53, 79, 265371653;
		

Links

• Charles R Greathouse IV, Rows n = 1..100 of triangle, flattened

Crossrefs

Cf. A002371, A046107.

Programs

PARI

go(n)=my(v=[],P=[],E=[],t,ok); for(k=1,n, t=setminus(factor(10^k-1)[,1]~,P); E=concat(E,vector(#t,i,1)); P=concat(P,t); E=apply(i->E[i],Vec(vecsort(P,,1))); P=vecsort(P); ok=1; while(ok, ok=0; for(i=1,#P,if(znorder(Mod(10,P[i]^(E[i]+1)))==k, E[i]++; t=concat(t,P[i]^E[i]); ok=1))); v=concat(v,t=vecsort(t)); print(k" "t)); v \\ Charles R Greathouse IV, Aug 01 2013

Extensions

a(9)-a(43) from Charles R Greathouse IV, Aug 01 2013