A001914 Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2. (Formerly M2940 N1183)

2, 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

Offset

1,1

Comments

Also, apart from first term 2, primes p for which the repunit (A002275) R((p-1)/2)=(10^((p-1)/2)-1)/9 is the smallest repunit divisible by p. Primes for which A000040(n) = 2*A071126(n) + 1. - Hugo Pfoertner, Mar 18 2003, Sep 18 2018

References

Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: Dover, 1966. Pages 65, 309.

M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 61.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..1180

Example

The repunit R(6)=111111 is the smallest repunit divisible by the prime a(2)=13=2*6+1.

Prog

(PARI) R(n)=(10^n-1)/9;
print1(2, ", "); forprime(p=3, 1000, m=0; for(q=3, (p-1)/2-1, if(R(q)%p==0, m=1; break)); if(m==0&&R((p-1)/2)%p==0, print1(p, ", "))) \\ Hugo Pfoertner, Sep 18 2018

Crossrefs

Cf. A003277 for another sequence of cyclic numbers.

Cf. A000040, A002275, A071126.

Sequence in context: A030452 A132602 A359125 * A254447 A031392 A156980

Adjacent sequences: A001911 A001912 A001913 * A001915 A001916 A001917

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Enoch Haga

Status

approved