A101075 Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 21 for n > 0.

0, 2, 16, 18, 32, 38, 168, 452, 610, 882, 1472, 6510, 9646, 21592, 39990, 40156, 71502

Offset

1,2

Comments

Numbers k such that (780*10^k + 21)/9 is prime.

Numbers k such that digit 8 followed by k >= 0 occurrences of digit 6 followed by digit 9 is prime.

Numbers corresponding to terms <= 882 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..17.

Makoto Kamada, Prime numbers of the form 866...669.

Index entries for primes involving repunits.

Formula

a(n) = A103088(n+1) - 1. [adapted by Georg Fischer, Jan 04 2021]

Example

8669 is prime, hence 2 is a term.

Mathematica

Flatten[Position[NestList[10#-21&, 89, 9700], _?PrimeQ]]-1 (* Harvey P. Dale, May 26 2012 *)

Prog

(PARI) a=89; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-21)
(PARI) for(n=0, 1500, if(isprime((780*10^n+21)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103088.

Sequence in context: A282838 A180923 A058242 * A022370 A161802 A323193

Adjacent sequences: A101072 A101073 A101074 * A101076 A101077 A101078

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004

Extensions

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

a(14)-a(16) from Kamada data by Ray Chandler, Apr 29 2015

a(17) derived from A103088 by Elmo R. Oliveira, Dec 15 2025

Status

approved