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

1,1

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.

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..23.

Makoto Kamada, Prime numbers of the form 900...001.

Index entries for primes involving repunits.

Formula

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

Example

900001 is prime, hence 4 is a term.

Prog

(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, ", ")))

Crossrefs

Cf. A000533, A002275, A056797.

Sequence in context: A108506 A129284 A214700 * A368989 A128657 A105421

Adjacent sequences: A100994 A100995 A100996 * A100998 A100999 A101000

Keyword

nonn,hard,more

Author

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

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

Status

approved