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

1,1

Links

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

Example

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;

Prog

(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

Crossrefs

Cf. A002371, A046107.

Sequence in context: A003597 A018705 A018381 * A272704 A272737 A273533

Adjacent sequences: A227966 A227967 A227968 * A227970 A227971 A227972

Keyword

nonn,tabf,base

Author

J. Lowell, Aug 01 2013

Extensions

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

Status

approved