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

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

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

Examples

			72227 is prime, hence 3 is a term.
		

References

• Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

• Patrick De Geest, PDP Reference Table - 727.
• Makoto Kamada, Prime numbers of the form 722...227.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A082711.

Programs

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,",")))

Formula

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

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