A101528 Indices of primes in sequence defined by A(0) = 63, A(n) = 10*A(n-1) + 13 for n > 0.

1, 4, 5, 10, 14, 68, 89, 133, 188, 244, 266, 269, 469, 1574, 2294, 2506, 3511, 3824, 6856, 11021, 11656, 17498, 35035, 41965, 50557, 93061

Offset

1,2

Comments

Numbers n such that (580*10^n - 13)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.

Numbers corresponding to terms <= 469 are certified primes.

a(27) > 10^5. - Robert Price, Sep 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..26.

Makoto Kamada, Prime numbers of the form 644...443.

Index entries for primes involving repunits.

Formula

a(n) = A103035(n+1) - 1.

Example

6444443 is prime, hence 5 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(580*10^# - 13)/9] &] (* Robert Price, Sep 12 2015 *)

Prog

(PARI) a=63; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a+13)
(PARI) for(n=0, 1000, if(isprime((580*10^n-13)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103035.

Sequence in context: A116930 A073119 A002257 * A119040 A287578 A135104

Adjacent sequences: A101525 A101526 A101527 * A101529 A101530 A101531

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(20)-a(24) from Kamada data by Ray Chandler, Apr 30 2015

a(25)-a(26) from Robert Price, Sep 12 2015

Status

approved