A001914 Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.

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

Author

N. J. A. Sloane

Keywords

• nonn

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

Examples

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

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

Crossrefs

Cf. A003277 for another sequence of cyclic numbers.

Cf. A000040, A002275, A071126.

Programs

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

Extensions

More terms from Enoch Haga