A028416 -id:A028416 - cp's OEIS frontend

A284602 Numbers k such that the decimal representation of 1/k is either finite or has even period.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 32, 33, 34, 35, 38, 39, 40, 42, 44, 46, 47, 49, 50, 51, 52, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 68, 69, 70, 73, 76, 77, 78, 80, 84, 85, 87, 88, 89, 91, 92, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 109, 110, 112, 113, 114, 115

Offset: 1

Ilya Gutkovskiy, Mar 30 2017

All numbers of the form 2^i*5^j with i, j >= 0 are in this sequence (numbers with a finite decimal expansion).
From Robert G. Wilson v, Apr 02 2017: (Start)
If k is in the sequence, then so are 2k and 5k.
The complement of A284601.
Primitives: 1, 7, 11, 13, 17, 19, 21, 23, 29, 33, 39, 47, 49, 51, 57, 59, 61, 63, ..., .
(End)

			14 is in the sequence because 1/14 = 0.0714285(714285)..., whose period is 6, an even number.

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Index entries for sequences related to decimal expansion of 1/n

Cf. A002371, A003592, A028416, A051626, A206586, A284601.

Select[Range[115], Mod[Length[RealDigits[1/#][[1, -1]]], 2] == 0 & ]

A019365 Primes with primitive root 40.

Original entry on oeis.org

7, 11, 17, 19, 23, 29, 47, 59, 73, 97, 101, 103, 109, 131, 137, 139, 149, 167, 179, 193, 229, 233, 257, 263, 269, 331, 349, 353, 383, 389, 421, 433, 461, 463, 491, 499, 503, 509, 541, 571, 577, 593, 607, 617, 619, 659, 661, 673, 701, 709, 727, 743, 829, 857, 859, 863

Offset: 1

David W. Wilson

nonn

Subsequence of A028416. - Davide Rotondo, Dec 31 2024

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for primes by primitive root

Cf. A028416.

pr=40; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]

isok(p) = isprime(p) && (gcd(p,40)==1) && (znorder(Mod(40, p)) == p-1); \\ Michel Marcus, Jan 26 2025

A186640 Primes p such that the decimal expansion of 1/p has a periodic part of even length, but are not cyclic numbers (A001913).

Original entry on oeis.org

11, 13, 73, 89, 101, 103, 127, 137, 139, 157, 197, 211, 241, 251, 281, 293, 331, 349, 353, 373, 401, 409, 421, 449, 457, 463, 521, 557, 569, 601, 607, 617, 641, 653, 661, 673, 677, 691, 739, 761, 769, 809, 829, 859, 877, 881, 929, 967, 997, 1009, 1049, 1061

Offset: 1

Jani Melik, Feb 24 2011

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A028416.

f1_d := proc(n) local st, period:
st := ithprime(n):
period := numtheory[order](10,st):
if (modp(period,2) = 0) then
   if (st-1 <> period) then
      RETURN(st):
   fi:
fi: end:  seq(f1_d(n), n=1..200);

Select[Prime[Range[200]], EvenQ[Length[RealDigits[1/#][[1, 1]]]] && MultiplicativeOrder[10, #] != # - 1 &] (* T. D. Noe, Oct 01 2012 *)

is(p)=if(p>9 && isprime(p), my(o=znorder(Mod(10, p))); o%2==0 && o+1!=p, 0) \\ Charles R Greathouse IV, Oct 01 2012

p in A028416, but not A001913.

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A284602 Numbers k such that the decimal representation of 1/k is either finite or has even period.

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A019365 Primes with primitive root 40.

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A186640 Primes p such that the decimal expansion of 1/p has a periodic part of even length, but are not cyclic numbers (A001913).

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