A101056 Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) - 27 for n > 0.

0, 30, 104, 112, 368, 1358, 6218, 105570, 150974

Offset

1,2

Comments

Numbers n such that 80*10^n + 3 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.

Numbers corresponding to terms <= 368 are certified primes.

a(10) > 2*10^5. - Robert Price Aug 19 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..9.

Makoto Kamada, Prime numbers of the form 800...003.

Index entries for primes involving repunits.

Formula

a(n) = A103069(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

83 is prime, hence 0 is a term.

Mathematica

Select[Range[0, 20000], PrimeQ[80*10^# + 3] &] (* Robert Price, Aug 19 2015 *)

Prog

(PARI) a=83; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-27)
(PARI) for(n=0, 1500, if(isprime(80*10^n+3), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103069.

Sequence in context: A043218 A039395 A043998 * A316362 A081370 A257891

Adjacent sequences: A101053 A101054 A101055 * A101057 A101058 A101059

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004

Extensions

6218 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(8) - a(9) from Robert Price, Aug 19 2015

Status

approved