A101724 Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 33 for n > 0.

0, 2, 4, 5, 7, 14, 25, 52, 59, 96, 182, 204, 301, 395, 455, 466, 606, 827, 1859, 2742, 4272, 4780, 5711, 6037, 6636, 9221, 10831, 18864, 25847, 42246, 48546, 87564, 95587

Offset

1,2

Comments

Numbers n such that (390*10^n + 33)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 3 followed by digit 7 is prime.

Numbers corresponding to terms <= 827 are certified primes.

a(34) > 10^5. - Robert Price, May 11 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..33.

Makoto Kamada, Prime numbers of the form 433...337.

Index entries for primes involving repunits.

Formula

a(n) = A102989(n) - 1.

Example

4337 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 300], PrimeQ[(390*10^# + 33)/9] &] (* Robert Price, May 11 2015 *)

Prog

(PARI) a=47; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-33)
(PARI) for(n=0, 1500, if(isprime((390*10^n+33)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102989.

Sequence in context: A115883 A063508 A356849 * A123210 A019277 A127791

Adjacent sequences: A101721 A101722 A101723 * A101725 A101726 A101727

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Extensions

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

a(27)-a(31) from Kamada data by Ray Chandler, Apr 30 2015

a(32)-a(33) from Robert Price, May 11 2015

Status

approved