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A097443 Half-period primes, i.e., primes p for which the decimal expansion of 1/9 has period (p-1)/2. 8
3, 13, 31, 43, 67, 71, 83, 89, 107, 151, 157, 163, 191, 197, 199, 227, 283, 293, 307, 311, 347, 359, 373, 401, 409, 431, 439, 443, 467, 479, 523, 557, 563, 569, 587, 599, 601, 631, 653, 677, 683, 719, 761, 787, 827, 839, 877, 881, 883, 911, 919, 929, 947, 991 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or, primes p for which 10 has multiplicative order (p-1)/2. - Robert Israel, Jul 15 2016

LINKS

Table of n, a(n) for n=1..54.

Robert Israel, Table of n, a(n) for n = 1..10000 (Terms 2..1001 from T. D. Noe.)

Makoto Kamada, Factorizations of 11...11 (Repunit).

Index entries for sequences related to decimal expansion of 1/n

EXAMPLE

13 is a half-period prime because 1/13 = 0.076923076923076923076923... i.e., has period 6, or (13-1)/2.

MAPLE

select(t -> isprime(t) and numtheory:-order(10, t) = (t-1)/2,

[seq(t, t = 3..1000, 2)]); - Robert Israel, Jul 15 2016

MATHEMATICA

f[n_Integer] := Block[{ds = Divisors[n - 1]}, (n - 1)/Take[ ds, Position[ PowerMod[ 10, ds, n], 1] [[1, 1]]] [[ -1]]]; Select[ Prime[ Range[4, 200]], f[ # ] == 2 &] (* Robert G. Wilson v, Sep 14 2004 *)

PROG

(PARI) is(n)= gcd(10, n)==1 && isprime(n) && znorder(Mod(10, n))==(n-1)/2 \\ Dana Jacobsen, Jul 19 2016

(Perl) use ntheory ":all"; forprimes { say if znorder(10, $_) == ($_-1)/2; } 1, 1000; # Dana Jacobsen, Jul 19 2016

CROSSREFS

Almost the same as A001914.

Cf. A001913, A055628, A056157, A056210-A056217, A098680

Cf. also A000040, A007732, A006883, A097443, A097955.

Sequence in context: A077717 A235265 A275081 * A248368 A171517 A179026

Adjacent sequences:  A097440 A097441 A097442 * A097444 A097445 A097446

KEYWORD

nonn,changed

AUTHOR

Julien Peter Benney (jpbenney(AT)ftml.net), Aug 23 2004

EXTENSIONS

Edited (including prepending 3) by N. J. A. Sloane, Oct 19 2018 at the suggestion of Georg Fischer.

STATUS

approved

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Last modified October 23 10:33 EDT 2018. Contains 316525 sequences. (Running on oeis4.)