A056258 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 23 for n > 0.

9, 29, 119, 483, 1485, 1577, 13671, 13809, 15093, 72771, 94211, 207555, 1116675

Offset

1,1

Comments

Numbers k such that (670*10^k + 23)/9 is prime.

Numbers k such that digit 7 followed by k >= 0 occurrences of digit 4 followed by digit 7 is prime.

Numbers corresponding to terms <= 1577 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

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..13.

Patrick De Geest, PDP Reference Table - 747.

Makoto Kamada, Prime numbers of the form 744...447.

Index entries for primes involving repunits.

Formula

a(n) = A082712(n) - 2.

Example

74444444447 is prime, hence 9 is a term.

Mathematica

Select[Range[0, 2000], PrimeQ[(670 10^# + 23) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

Prog

(PARI) a=77; for(n=0, 1600, if(isprime(a), print1(n, ", ")); a=10*a-23)
(PARI) for(n=0, 1600, if(isprime((670*10^n+23)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A082712.

Sequence in context: A288744 A183245 A101141 * A147282 A146602 A146413

Adjacent sequences: A056255 A056256 A056257 * A056259 A056260 A056261

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Aug 18 2000

Extensions

Edited by Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

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

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

Edited by Ray Chandler, Nov 05 2014

a(12)-a(13) derived from A082712 by Elmo R. Oliveira, Dec 14 2025

Status

approved