A101017 Indices of primes in sequence defined by A(0) = 93, A(n) = 10*A(n-1) + 53 for n > 0.

1, 2, 31, 41, 74, 367, 1391, 16349, 49100, 49688, 91839

Offset

1,2

Comments

Numbers n such that (890*10^n - 53)/9 is prime.

Numbers n such that digit 9 followed by n >= 0 occurrences of digit 8 followed by digit 3 is prime.

Numbers corresponding to terms <= 367 are certified primes.

a(12) > 10^5. - Robert Price, Nov 12 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..11.

Makoto Kamada, Prime numbers of the form 988...883.

Index entries for primes involving repunits.

Formula

a(n) = A103108(n) - 1.

Example

9883 is prime, hence 2 is a term.

Mathematica

Flatten[Position[NestList[10#+53&, 93, 1500], _?(PrimeQ[#]&)]]-1
Select[Range[0, 100000], PrimeQ[(890*10^# - 53)/9] &] (* Robert Price, Nov 12 2015 *)

Prog

(PARI) a=93; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+53)
(PARI) for(n=0, 1500, if(isprime((890*10^n-53)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103108.

Sequence in context: A264783 A215031 A120638 * A207973 A193423 A241484

Adjacent sequences: A101014 A101015 A101016 * A101018 A101019 A101020

Keyword

nonn,hard,more

Author

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

Extensions

a(8)-a(10) from Kamada data by Ray Chandler, Apr 29 2015

a(11) from Robert Price, Nov 12 2015

Status

approved