A101541 Indices of primes in sequence defined by A(0) = 61, A(n) = 10*A(n-1) + 81 for n > 0.

0, 1, 2, 3, 13, 14, 22, 27, 53, 99, 271, 372, 402, 567, 638, 841, 968, 1254, 1258, 3046, 4837, 6388, 12754, 15141, 34942, 37651, 38107, 38685, 39383, 43392, 47279, 55029, 161191, 226478

Offset

1,3

Comments

Numbers n such that (630*10^n - 81)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 9 followed by digit 1 is prime.

Numbers corresponding to terms <= 968 are certified primes.

a(35) > 3*10^5. - Robert Price, Jul 10 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..34.

Makoto Kamada, Prime numbers of the form 699...991.

Index entries for primes involving repunits.

Formula

a(n) = A103048(n) - 1.

Example

69991 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(630*10^# - 81)/9] &] (* Robert Price, Oct 14 2015 *)

Prog

(PARI) a=61; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+81)
(PARI) for(n=0, 1500, if(isprime((630*10^n-81)/9), print1(n, ", ")))
(Magma) [n: n in [0..500] | IsPrime((630*10^n-81) div 9)]; // Vincenzo Librandi, Oct 15 2015

Crossrefs

Cf. A000533, A002275, A103048.

Sequence in context: A250184 A128460 A273617 * A299543 A059670 A038975

Adjacent sequences: A101538 A101539 A101540 * A101542 A101543 A101544

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(25)-a(32) from Kamada data by Ray Chandler, Apr 30 2015

a(33) from Robert Price, Oct 14 2015

a(34) from Robert Price, Jul 10 2023

Status

approved