A102011 Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 61 for n > 0.

0, 2, 5, 50, 56, 62, 149, 392, 419, 546, 42023, 43062, 101612, 107384

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (110*10^n + 61)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.

Numbers corresponding to terms <= 546 are certified primes.

a(13) > 10^5. - Robert Price, Jan 17 2015

a(15) > 2*10^5. - Tyler Busby, Feb 01 2023

Examples

			1222229 is prime, hence 5 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 122...229.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A102931.

Programs

PARI

a=19;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-61)

PARI

for(n=0,1500,if(isprime((110*10^n+61)/9),print1(n,",")))

Formula

a(n) = A102931(n) - 1.

Extensions

a(11)-a(12) derived from A102931 by Robert Price, Jan 17 2015

a(13)-a(14) from Tyler Busby, Jan 31 2023