A101970 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) + 53 for n > 0.

0, 1, 6, 27, 72, 294, 493, 597, 2599, 3729, 7548, 15864

Offset

1,3

Comments

Numbers n such that (260*10^n - 53)/9 is prime.

Numbers n such that digit 2 followed by n >= 0 occurrences of digit 8 followed by digit 3 is prime.

Numbers corresponding to terms <= 597 are certified primes.

a(13) > 10^5. - Robert Price, Apr 18 2014

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..12.

Makoto Kamada, Prime numbers of the form 288...883.

Index entries for primes involving repunits.

Formula

a(n) = A102961(n) - 1. [adapted by Georg Fischer, Jan 04 2021]

Example

283 is prime, hence 1 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(260*10^# - 53)/9] &] (* Robert Price, Apr 18 2015 *)

Prog

(PARI) a=23; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+53)
(PARI) for(n=0, 1500, if(isprime((260*10^n-53)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102961.

Sequence in context: A273408 A085788 A027276 * A136105 A239568 A198958

Adjacent sequences: A101967 A101968 A101969 * A101971 A101972 A101973

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) derived from A102961 by Robert Price, Apr 18 2015

Status

approved