A100997 Indices of primes in sequence defined by A(0) = 91, A(m) = 10*A(m-1) - 9 for m > 0.

2, 3, 4, 8, 21, 26, 35, 56, 61, 77, 200, 536, 695, 789, 904, 1037, 66885, 70499, 91835, 100612, 127239, 380733, 583695

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 26 2004

Keywords

• nonn
• hard
• more

Comments

Numbers k such that 90*10^k + 1 is prime.

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

Numbers corresponding to terms <= 1037 are certified primes.

Examples

			900001 is prime, hence 4 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 900...001.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A056797.

Programs

PARI

a=91;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-9)

PARI

for(n=0,1500,if(isprime(90*10^n+1),print1(n,",")))

Formula

a(n) = A056797(n) - 1.

Extensions

66885 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(18)-a(21) from Kamada data by Ray Chandler, Apr 28 2015

a(22)-a(23) from Kamada data by Mohammed Yaseen, Jul 20 2021