A101951 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 27 for n > 0.

0, 2, 4, 5, 6, 11, 15, 16, 21, 23, 34, 114, 119, 357, 1487, 1818, 4678, 9820, 27216, 27692, 194412

Offset

1,2

Comments

Numbers n such that 20*10^n + 3 is prime.

Numbers n such that digit 2 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.

Numbers corresponding to terms <= 357 are certified primes.

a(21) > 10^5. - Robert Price, Nov 16 2014

a(22) > 2*10^5. - Robert Price, Jul 11 2015

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..21.

Makoto Kamada, Prime numbers of the form 200...003.

Formula

a(n) = A081677(n+1) - 1. - Robert Price, Nov 16 2014

Example

2003 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 1000], PrimeQ[(20 10^# + 3)] &] (* Vincenzo Librandi, Nov 17 2014 *)

Prog

(PARI) a=23; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-27)
(PARI) for(n=0, 1500, if(isprime(20*10^n+3), print1(n, ", ")))
(Magma) [n: n in [0..500] | IsPrime(20*10^n+3)]; // Vincenzo Librandi, Nov 17 2014

Crossrefs

Cf. A000533, A002275, A081677.

Sequence in context: A113631 A202101 A192582 * A171166 A194607 A194637

Adjacent sequences: A101948 A101949 A101950 * A101952 A101953 A101954

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

Extensions

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

a(19)-a(20) derived from A081677 by Robert Price, Nov 16 2014

a(21) from Robert Price, Jul 11 2015

Status

approved