A101717 Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 53 for n > 0.

0, 3, 83, 164, 273, 512, 3371, 4176, 4317, 10578, 17220, 19671, 20064, 36645, 40190, 55358, 86229

Offset

1,2

Comments

Numbers n such that (370*10^n + 53)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 1 followed by digit 7 is prime.

Numbers corresponding to terms <= 512 are certified primes.

a(18) > 10^5. - Robert Price, May 10 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..17.

Makoto Kamada, Prime numbers of the form 411...117.

Index entries for primes involving repunits.

Formula

a(n) = A102982(n) - 1.

Example

41117 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 3000], PrimeQ[(370*10^# + 53)/9] &] (* Robert Price, May 10 2015 *)

Prog

(PARI) a=47; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-53)
(PARI) for(n=0, 1500, if(isprime((370*10^n+53)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102982.

Sequence in context: A385792 A139897 A085318 * A053974 A239637 A201963

Adjacent sequences: A101714 A101715 A101716 * A101718 A101719 A101720

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(10)-a(15) from Kamada data by Ray Chandler, Apr 30 2015

a(16)-a(17) from Robert Price, May 10 2015

Status

approved