A056260 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 3 for n > 0. Numbers n such that (690*10^n + 3)/9 is prime.

3, 5, 53, 95, 453, 573, 3383, 11439, 12623, 19445, 35459, 81213, 95325

Offset

1,1

Comments

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 6 followed by digit 7 is prime.

Numbers corresponding to terms <= 3383 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..13.

Patrick De Geest, PDP Reference Table - 767.

Makoto Kamada, Prime numbers of the form 766...667.

Formula

a(n) = A082714(n) - 2.

Example

76667 is prime, hence 3 is a term.

Mathematica

Select[Range[3500], PrimeQ[(690 10^# + 3) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

Prog

(PARI) a=77; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-3)
(PARI) for(n=0, 1000, if(isprime((690*10^n+3)/9), print1(n, ", ")))
(Magma) [n: n in [0..300] | IsPrime((690*10^n+3) div 9)]; // Vincenzo Librandi, Nov 03 2014

Crossrefs

Cf. A000533, A002275, A082714.

Sequence in context: A260227 A260226 A101149 * A213052 A355016 A260223

Adjacent sequences: A056257 A056258 A056259 * A056261 A056262 A056263

Keyword

hard,nonn

Author

Robert G. Wilson v, Aug 18 2000

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Apr 29 2007, Jun 15 2007

a(7)-a(11) from Robert G. Wilson v, May 02 2007

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

Edited by Ray Chandler, Nov 05 2014

Status

approved