A101848 Indices of primes in sequence defined by A(0) = 31, A(n) = 10*A(n-1) + 81 for n > 0.

0, 16, 18, 28, 42, 118, 172, 948, 1608, 5578, 19678, 34146, 43492, 97798

Offset

1,2

Comments

Numbers n such that (360*10^n - 81)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 9 followed by digit 1 is prime.

Numbers corresponding to terms <= 948 are certified primes.

a(15) > 10^5. - Robert Price, Mar 17 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..14.

Makoto Kamada, Prime numbers of the form 399...991.

Index entries for primes involving repunits.

Formula

a(n) = A101396(n) - 1.

Example

31 is prime, hence 0 is a term.

Mathematica

Select[Range[0, 1000], PrimeQ[(360*10^# - 81)/9] &] (* Robert Price, Mar 17 2015 *)

Prog

(PARI) a=31; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+81)
(PARI) for(n=0, 1500, if(isprime((360*10^n-81)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A101396.

Sequence in context: A057369 A178110 A117100 * A032401 A335223 A334453

Adjacent sequences: A101845 A101846 A101847 * A101849 A101850 A101851

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004

Extensions

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

a(12)-a(14) derived from A101396 by Robert Price, Mar 17 2015

Status

approved