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 A227969 Powers of primes other than 2 and 5 in order by cycle length of reciprocal in decimal. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 18 21:04 EST 2018. Contains 317331 sequences. (Running on oeis4.)