A056257 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 43 for n > 0.

1, 3, 7, 27, 63, 723, 1785, 7275, 19461, 24213, 51777, 131391

Offset

1,2

Comments

Numbers n such that (650*10^n + 43)/9 is prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 2 followed by digit 7 is prime.

Numbers corresponding to terms <= 1785 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

a(13) > 200000. - Tyler Busby, Jan 14 2023

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..12.

Patrick De Geest, PDP Reference Table - 727.

Makoto Kamada, Prime numbers of the form 722...227.

Index entries for primes involving repunits.

Formula

a(n) = A082711(n) - 2.

Example

72227 is prime, hence 3 is a term.

Prog

(PARI) a=77; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-43)
(PARI) for(n=0, 1000, if(isprime((650*10^n+43)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A082711.

Sequence in context: A272530 A225038 A293564 * A066021 A259595 A148742

Adjacent sequences: A056254 A056255 A056256 * A056258 A056259 A056260

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Aug 18 2000

Extensions

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

One more term added from PDP table and comments section updated by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 05 2014

a(12) from Tyler Busby, Jan 11 2023

Status

approved