A101956 Indices of primes in sequence defined by A(0) = 29, A(n) = 10*A(n-1) - 51 for n > 0.

0, 1, 2, 3, 7, 10, 12, 23, 27, 51, 53, 93, 296, 656, 1005, 5346, 8188, 9313, 23054, 53286, 64806

Offset

1,3

Comments

Numbers n such that (210*10^n + 51)/9 is prime.

Numbers n such that digit 2 followed by n >= 0 occurrences of digit 3 followed by digit 9 is prime.

Numbers corresponding to terms <= 656 are certified primes.

a(22) > 10^5. - Robert Price, Nov 25 2014

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 233...339.

Index entries for primes involving repunits.

Formula

a(n) = A102951(n) - 1. - Robert Price, Nov 25 2014

Example

2339 is prime, hence 2 is a term.

Mathematica

Transpose[Select[Partition[With[{no=10000}, Riffle[NestList[10#-51&, 29, no], Range[0, no]]], 2], PrimeQ[First[#]]&]][[2]]  (* Harvey P. Dale, Feb 05 2011 *)

Prog

(PARI) a=29; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-51)
(PARI) for(n=0, 1500, if(isprime((210*10^n+51)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102951.

Sequence in context: A140512 A285550 A171863 * A273064 A341238 A002238

Adjacent sequences: A101953 A101954 A101955 * A101957 A101958 A101959

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(21) derived from A102951 by Robert Price, Nov 25 2014

Status

approved