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

Author

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

Keywords

• nonn
• hard
• more

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

Examples

			911111111111111117 is prime, hence 16 is a term.
		

References

• Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

• Makoto Kamada, Prime numbers of the form 911...117.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A100473.

Programs

Mathematica

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

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,",")))

Formula

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

Extensions

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