A060282 Periodic part of decimal expansion of reciprocal of n-th prime (leading 0's omitted).

0, 3, 0, 142857, 9, 76923, 588235294117647, 52631578947368421, 434782608695652173913, 344827586206896551724137931, 32258064516129, 27, 2439, 23255813953488372093, 212765957446808510638297872340425531914893617

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n=1..100

Formula

a(n) = floor(10^A002371(n)/prime(n)).

a(n) = 0 if and only if n = 1 or 3, corresponding to the primes 2 and 5, which are factors of 10. - Alonso del Arte, Apr 03 2020

ceiling(log_10(a(n))) = prime(n) - 1 if prime(n) is a full reptend prime (A001913). - Alonso del Arte, Apr 14 2020

Example

1/7 = 0.142857142..., so a(4) = 142857.
1/11 = 0.09090909..., so a(5) = 9.

Mathematica

primePer[1] = primePer[3] = 0; primePer[n_] := FromDigits[(d = RealDigits[1/Prime[n]])[[1, 1]]] * 10^d[[2]]; Array[ primePer, 15] (* Amiram Eldar, Apr 28 2020 *)

Prog

(PARI) f(n)=if(n<4, n==2, znorder(Mod(10, prime(n)))) \\ A002371
for(n=1, 100, print1(floor(10^f(n)/prime(n)), ", "))

Crossrefs

Cf. A002371, A036275, A060283, A060251, A036275, A001913.

Sequence in context: A266380 A076951 A359561 * A060283 A255851 A334743

Adjacent sequences: A060279 A060280 A060281 * A060283 A060284 A060285

Keyword

nonn,easy,base

Author

N. J. A. Sloane, Mar 30 2001

Extensions

More terms from Klaus Brockhaus, Mar 30 2001

Status

approved