A101590 Indices of primes in sequence defined by A(0) = 53, A(n) = 10*A(n-1) + 63 for n > 0.

0, 1, 4, 5, 6, 10, 16, 28, 41, 46, 95, 107, 165, 209, 330, 1021, 3592, 4425, 5703, 13935, 16485, 85909

Offset

1,3

Comments

Numbers n such that (540*10^n - 63)/9 is prime.

Numbers n such that digit 5 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

Numbers corresponding to terms <= 330 are certified primes.

a(23) > 2*10^5. - Robert Price, Aug 07 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..22.

Makoto Kamada, Prime numbers of the form 599...993.

Index entries for primes involving repunits.

Formula

a(n) = A103025(n) - 1.

Example

593 is prime, hence 1 is a term.

Mathematica

Select[Range[0, 200000], PrimeQ[(540*10^# - 63)/9] &] (* Robert Price, Aug 07 2015 *)

Prog

(PARI) a=53; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+63)
(PARI) for(n=0, 1500, if(isprime((540*10^n-63)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103025.

Sequence in context: A347806 A079257 A001609 * A057916 A249853 A162415

Adjacent sequences: A101587 A101588 A101589 * A101591 A101592 A101593

Keyword

nonn,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 09 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(20)-a(22) from Kamada data by Ray Chandler, Apr 30 2015

Status

approved