A101973 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) + 63 for n > 0.

0, 1, 4, 9, 28, 38, 113, 483, 864, 4179, 5384, 13121, 13831, 22675, 25019, 30056, 35909, 37934, 42294, 50193, 110075, 184123, 191151

Offset

1,3

Comments

Numbers n such that (270*10^n - 63)/9 is prime.

Numbers n such that digit 2 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

Numbers corresponding to terms <= 864 are certified primes.

a(21) > 10^5. - Robert Price, Jan 25 2015

a(24) > 2*10^5. - Robert Price, Aug 09 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..23.

Makoto Kamada, Prime numbers of the form 299...993.

Index entries for primes involving repunits.

Formula

a(n) = A102964(n) - 1.

Example

293 is prime, hence 1 is a term.

Mathematica

Select[Range[0, 200000], PrimeQ[(270*10^# - 63)/9] &] (* Robert Price, Aug 09 2015 *)

Prog

(PARI) a=23; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+63)
(PARI) for(n=0, 1500, if(isprime((270*10^n-63)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102964.

Sequence in context: A270891 A272313 A239668 * A244968 A071258 A120333

Adjacent sequences: A101970 A101971 A101972 * A101974 A101975 A101976

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

Extensions

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

a(12)-a(20) derived from A102964 by Robert Price, Jan 25 2015

a(21)-a(23) derived from A102964 by Robert Price, Aug 09 2015

Status

approved