A103007 Numbers n such that 5*10^n + R_n + 8 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

0, 1, 3, 7, 15, 22, 189, 445, 543, 633, 757, 8725, 9003, 37402

Offset

1,3

Comments

Also numbers n such that (46*10^n+71)/9 is prime (including 0).

a(15) > 10^5. - Robert Price, Jul 13 2015

Links

Table of n, a(n) for n=1..14.

Makoto Kamada, Prime numbers of the form 511...119.

Index entries for primes involving repunits.

Formula

a(n) = A101572(n-1) + 1, for n>1.

Maple

A103007:=n->`if`(isprime((46*10^n+71)/9), n, NULL): seq(A103007(n), n=0..1000); # Wesley Ivan Hurt, Aug 06 2015

Mathematica

Do[ If[ PrimeQ[(46*10^n + 71)/9], Print[n]], {n, 0, 10000}]

Prog

(PARI) repunit(n)=my(r=""); if(n>0, for(i=1, n, r=concat(r, "1"))); eval(r);
first(m)=my(v=vector(m), t=0); for(i=1, m, while(!isprime((5*10^t + repunit(t) + 8 )), t++); v[i]=t; t++; ); v /* Anders Hellström, Aug 06 2015 */
(Magma) [n: n in [0..300]| IsPrime((46*10^n+71) div 9)]; // Vincenzo Librandi, Aug 05 2015

Crossrefs

Cf. A002275, A101572.

Sequence in context: A015821 A229527 A091711 * A077790 A322971 A165469

Adjacent sequences: A103004 A103005 A103006 * A103008 A103009 A103010

Keyword

more,nonn

Author

Robert G. Wilson v, Jan 18 2005

Extensions

a(14) found by Erik Branger on May 01 2013, submitted by Ray Chandler, Aug 16 2013

a(1) = 0 prepended by Robert Price, Jul 13 2015

Status

approved