A100999 Indices of primes in sequence defined by A(0) = 97, A(n) = 10*A(n-1) - 53 for n > 0.

0, 16, 22, 72, 130, 472, 684, 700, 1908, 3028, 3472, 4192, 9930

Offset

1,2

Comments

Numbers n such that (820*10^n + 53)/9 is prime.

Numbers n such that digit 9 followed by n >= 0 occurrences of digit 1 followed by digit 7 is prime.

Numbers corresponding to terms <= 700 are certified primes.

a(14) > 10^5. - Robert Price, Oct 25 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 911...117.

Index entries for primes involving repunits.

Formula

a(n) = A100473(n) - 1.

Example

911111111111111117 is prime, hence 16 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(820*10^# + 53)/9] &] (* Robert Price, Oct 25 2015 *)

Prog

(PARI) a=97; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-53)
(PARI) for(n=0, 1000, if(isprime((820*10^n+53)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A100473.

Sequence in context: A305337 A322344 A316417 * A304923 A306163 A317380

Adjacent sequences: A100996 A100997 A100998 * A101000 A101001 A101002

Keyword

nonn,hard,more

Author

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

Extensions

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

Status

approved