A101579 Indices of primes in sequence defined by A(0) = 53, A(n) = 10*A(n-1) + 13 for n > 0.

0, 2, 3, 8, 11, 59, 267, 288, 383, 794, 3473, 9179, 76437

Offset

1,2

Comments

Numbers n such that (490*10^n - 13)/9 is prime.

Numbers n such that digit 5 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.

Numbers corresponding to terms <= 794 are certified primes.

a(14) > 10^5. - Robert Price, Jul 16 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..13.

Makoto Kamada, Prime numbers of the form 544...443.

Index entries for primes involving repunits.

Formula

a(n) = A103014(n) - 1.

Example

54443 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(490*10^#-13)/9]&]

Prog

(PARI) a=53; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a+13)
(PARI) for(n=0, 1000, if(isprime((490*10^n-13)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103014.

Sequence in context: A119197 A119185 A056922 * A041711 A127939 A041587

Adjacent sequences: A101576 A101577 A101578 * A101580 A101581 A101582

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(13) from Robert Price, Jul 16 2015

Status

approved