A101526 Indices of primes in sequence defined by A(0) = 67, A(n) = 10*A(n-1) - 33 for n > 0.

0, 2, 3, 4, 5, 9, 12, 57, 95, 177, 359, 419, 454, 1007, 1516, 2974, 3998, 5424, 10818, 16035, 32075, 47236, 111384, 190934

Offset

1,2

Comments

Numbers n such that (570*10^n + 33)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 3 followed by digit 7 is prime.

Numbers corresponding to terms <= 454 are certified primes.

a(25) > 3*10^5 - Robert Price, Oct 26 2023

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..24.

Makoto Kamada, Prime numbers of the form 633...337.

Index entries for primes involving repunits.

Formula

a(n) = A103033(n) - 1.

Example

633337 is prime, hence 4 is a term.

Prog

(PARI) a=67; for(n=0, 1200, if(isprime(a), print1(n, ", ")); a=10*a-33)
(PARI) for(n=0, 1200, if(isprime((570*10^n+33)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103033.

Sequence in context: A033084 A076134 A239742 * A264994 A331364 A319720

Adjacent sequences: A101523 A101524 A101525 * A101527 A101528 A101529

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

Extensions

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

a(19)-a(22) from Kamada data by Ray Chandler, Apr 30 2015

a(23)-a(24) from Robert Price, Oct 26 2023

Status

approved