A056263 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) + 27 for n > 0.

1, 3, 27, 155, 321, 351, 1211, 1283, 7983, 15191, 84771, 119929, 148859

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• more

Comments

Numbers n such that (720*10^n - 27)/9 is a prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 9 followed by digit 7 is a prime.

Numbers corresponding to terms <= 1283 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

Examples

			797 is a prime, hence 1 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 - 797.
• Makoto Kamada, Prime numbers of the form 799...997.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A082716.

Programs

PARI

a=77;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+27)

PARI

for(n=0,1500,if(isprime((720*10^n-27)/9),print1(n,",")))

Formula

a(n) = A082716(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

Update from De Geest link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(11)=84771 from Ray Chandler, Jan 04 2011

a(12)=119929 from Ray Chandler, Apr 01 2011

a(13)=148859 from Ray Chandler, Apr 09 2011

Updated comments section by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 04 2014