A102033 Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) + 63 for n > 0.

0, 1, 2, 3, 5, 15, 20, 27, 47, 81, 121, 129, 281, 303, 4601, 12983, 13613, 42760, 90595, 109927, 158241

Offset

1,3

Comments

Numbers n such that (180*10^n - 63)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

Numbers corresponding to terms <= 303 are certified primes.

a(20) > 10^5. - Robert Price, Nov 16 2014

a(22) > 2*10^5. - Robert Price, Oct 25 2015

References

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

Table of n, a(n) for n=1..21.

Makoto Kamada, Prime numbers of the form 199...993.

Index entries for primes involving repunits.

Formula

a(n) = A102946(n) - 1. - Robert Price, Nov 16 2014

Example

193 is prime, hence 1 is a term.

Maple

A102033:=n->`if`(isprime((180*10^n-63)/9), n, NULL): seq(A102033(n), n=0..10^3); # Wesley Ivan Hurt, Nov 16 2014

Mathematica

Select[Range[0, 10^3], PrimeQ[(180*10^# - 63)/9] &] (* Wesley Ivan Hurt, Nov 16 2014 *)

Prog

(PARI) a=13; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+63)
(PARI) for(n=0, 1500, if(isprime((180*10^n-63)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102946.

Sequence in context: A155698 A099410 A330988 * A282616 A174418 A072246

Adjacent sequences: A102030 A102031 A102032 * A102034 A102035 A102036

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(18)-a(19) derived from A102946 by Robert Price, Nov 16 2014

a(20)-a(21) from Robert Price, Oct 25 2015

Status

approved