A101074 Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) + 33 for n > 0.

0, 1, 2, 12, 18, 61, 79, 125, 167, 194, 308, 409, 480, 607, 740, 878, 1175, 2687, 6235, 16293, 17316, 31573, 34860, 35391, 48725

Offset

1,3

Comments

Numbers n such that (780*10^n - 33)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 6 followed by digit 3 is prime.

Numbers corresponding to terms <= 878 are certified primes.

a(26) > 10^5. - Robert Price, Oct 25 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..25.

Makoto Kamada, Prime numbers of the form 866...663.

Index entries for primes involving repunits.

Formula

a(n) = A103087(n+1) - 1.

Example

8663 is prime, hence 2 is a term.

Mathematica

Flatten[Position[NestList[10#+33&, 83, 1000], _?PrimeQ]-1] (* To generate terms larger than 1000, increase the final constant in NestList. *) (* Harvey P. Dale, Oct 02 2012 *)
Select[Range[0, 100000], PrimeQ[(780*10^# - 33)/9] &] (* Robert Price, Oct 25 2015 *)

Prog

(PARI) a=83; for(n=0, 1200, if(isprime(a), print1(n, ", ")); a=10*a+33)
(PARI) for(n=0, 1200, if(isprime((780*10^n-33)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103087.

Sequence in context: A335799 A190044 A066238 * A115109 A048001 A109299

Adjacent sequences: A101071 A101072 A101073 * A101075 A101076 A101077

Keyword

nonn,hard,more

Author

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

Extensions

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

a(20)-a(25) from Kamada data by Ray Chandler, Apr 29 2015

Status

approved