A101066 Indices of primes in sequence defined by A(0) = 81, A(n) = 10*A(n-1) + 31 for n > 0.

25, 35, 37, 59, 79, 91, 173, 485, 626, 998, 1613, 4381, 4897, 8441, 17261, 17801, 35426, 40742

Offset

1,1

Comments

Numbers n such that (760*10^n - 31)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 4 followed by digit 1 is prime.

Numbers corresponding to terms <= 626 are certified primes.

a(19) > 10^5. - Robert Price, Oct 20 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..18.

Makoto Kamada, Prime numbers of the form 844...441.

Index entries for primes involving repunits.

Formula

a(n) = A103079(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

844444444444444444444444441 is prime, hence 25 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(760*10^# - 31)/9] &] (* Robert Price, Oct 20 2015 *)

Prog

(PARI) a=81; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a+31)
(PARI) for(n=0, 1000, if(isprime((760*10^n-31)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103079.

Sequence in context: A257720 A098368 A281370 * A340121 A061442 A049514

Adjacent sequences: A101063 A101064 A101065 * A101067 A101068 A101069

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004

Extensions

Three additional terms, corresponding to probable primes, from Ryan Propper, Jun 20 2005

One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Edited by T. D. Noe, Oct 30 2008

a(15)-a(18) from Kamada data by Ray Chandler, Apr 29 2015

Status

approved