A101070 Indices of primes in sequence defined by A(0) = 81, A(n) = 10*A(n-1) + 41 for n > 0.

20, 26, 59, 470, 1073, 5780

Offset

1,1

Comments

Numbers n such that (770*10^n - 41)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 5 followed by digit 1 is prime.

Numbers corresponding to terms <= 470 are certified primes.

a(7) > 10^5. - Robert Price, Oct 21 2015

It appears that a(n)+1 are all divisible by 3. - Robert Price, Oct 21 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..6.

Makoto Kamada, Prime numbers of the form 855...551.

Index entries for primes involving repunits.

Formula

a(n) = A103083(n) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

8555555555555555555551 is prime, hence 20 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(770*10^# - 41)/9] &] (* Robert Price, Oct 21 2015 *)
Flatten[Position[NestList[10#+41&, 81, 5800], _?(PrimeQ[#]&)]]-1 (* Harvey P. Dale, May 09 2018 *)

Prog

(PARI) a=81; for(n=0, 1200, if(isprime(a), print1(n, ", ")); a=10*a+41)
(PARI) for(n=0, 1200, if(isprime((770*10^n-41)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103083.

Sequence in context: A276503 A067065 A280307 * A219805 A219456 A248787

Adjacent sequences: A101067 A101068 A101069 * A101071 A101072 A101073

Keyword

nonn,hard,more

Author

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

Extensions

One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Status

approved