A101005 Indices of primes in sequence defined by A(0) = 97, A(n) = 10*A(n-1) - 33 for n > 0.

0, 1, 2, 3, 14, 26, 70, 85, 104, 241, 249, 447, 538, 783, 813, 1024, 1171, 1352, 3008, 3174, 3681, 6992, 7611, 7779, 9632, 27108, 27734, 28766, 61573

Offset

1,3

Comments

Numbers n such that (840*10^n + 33)/9 is prime.

Numbers n such that digit 9 followed by n >= 0 occurrences of digit 3 followed by digit 7 is prime.

Numbers corresponding to terms <= 1024 are certified primes.

a(30) > 10^5. - Robert Price, Nov 07 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..29.

Makoto Kamada, Prime numbers of the form 933...337.

Index entries for primes involving repunits.

Formula

a(n) = A103096(n+1) - 1.

Example

9337 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(840*10^# + 33)/9] &] (* Robert Price, Nov 07 2015 *)

Prog

(PARI) a=97; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-33)
(PARI) for(n=0, 1500, if(isprime((840*10^n+33)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103096.

Sequence in context: A047067 A112636 A124663 * A029998 A117461 A319670

Adjacent sequences: A101002 A101003 A101004 * A101006 A101007 A101008

Keyword

nonn,hard,more,less

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Extensions

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

a(26)-a(28) from Kamada data by Ray Chandler, Apr 28 2015

a(29) from Robert Price, Nov 07 2015

Status

approved