A101582 Indices of primes in sequence defined by A(0) = 53, A(n) = 10*A(n-1) + 33 for n > 0.

0, 1, 3, 6, 21, 27, 35, 108, 154, 867, 1776, 2464, 3873, 4505, 4683, 5502, 13974, 15631, 33053, 34306, 50494, 60630, 62327, 92512, 92868

Offset

1,3

Comments

Numbers n such that (510*10^n - 33)/9 is prime.

Numbers n such that digit 5 followed by n >= 0 occurrences of digit 6 followed by digit 3 is prime.

Numbers corresponding to terms <= 867 are certified primes.

a(26) > 10^5. - Robert Price, Jul 29 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..25.

Makoto Kamada, Prime numbers of the form 566...663.

Index entries for primes involving repunits.

Formula

a(n) = A103017(n+1) - 1.

Example

56663 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(510*10^# - 33)/9] &] (* Robert Price, Jul 29 2015 *)

Prog

(PARI) a=53; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a+33)
(PARI) for(n=0, 1000, if(isprime((510*10^n-33)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103017.

Sequence in context: A101719 A173165 A210504 * A069558 A174461 A050611

Adjacent sequences: A101579 A101580 A101581 * A101583 A101584 A101585

Keyword

nonn,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 09 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(17)-a(20) from Kamada data by Ray Chandler, Apr 30 2015

a(21)-a(25) from Robert Price, Jul 29 2015

Status

approved