A101725 Indices of primes in sequence defined by A(0) = 49, A(n) = 10*A(n-1) - 51 for n > 0.

1, 2, 5, 10, 14, 25, 27, 50, 149, 181, 227, 406, 637, 3580, 4124, 4982, 5665, 15889, 27742, 43361, 55366, 60743, 73700

Offset

1,2

Comments

Numbers n such that (390*10^n + 51)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 3 followed by digit 9 is prime.

Numbers corresponding to terms <= 637 are certified primes.

a(24) > 10^5. - Robert Price, Jun 25 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..23.

Makoto Kamada, Prime numbers of the form 433...339.

Index entries for primes involving repunits.

Formula

a(n) = A102990(n) - 1.

Example

4339 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 10000], PrimeQ[(390*10^# + 51)/9] &] (* Robert Price, Jun 25 2015 *)

Prog

(PARI) a=49; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-51)
(PARI) for(n=0, 1500, if(isprime((390*10^n+51)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102990.

Sequence in context: A082745 A064955 A352189 * A274453 A393935 A105370

Adjacent sequences: A101722 A101723 A101724 * A101726 A101727 A101728

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

a(21)-a(23) from Robert Price, Jun 25 2015

Status

approved