A101738 Indices of primes in sequence defined by A(0) = 41, A(n) = 10*A(n-1) + 81 for n > 0.

0, 1, 3, 6, 23, 171, 172, 217, 438, 2562, 2781, 2879, 3714, 4391, 10819, 14591, 25053, 27768, 40167, 180991, 193906

Offset

1,3

Comments

Numbers n such that (450*10^n - 81)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 9 followed by digit 1 is prime.

Numbers corresponding to terms <= 438 are certified primes.

a(22) > 2*10^5. - Robert Price, May 30 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..21.

Makoto Kamada, Prime numbers of the form 499...991.

Index entries for primes involving repunits.

Formula

a(n) = A103001(n) - 1.

Example

49991 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 1000], PrimeQ[(450*10^# - 81)/9] &] (* Robert Price, May 30 2015 *)

Prog

(PARI) a=41; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+81)
(PARI) for(n=0, 1500, if(isprime((450*10^n-81)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103001.

Sequence in context: A013211 A013212 A013218 * A083525 A106213 A129520

Adjacent sequences: A101735 A101736 A101737 * A101739 A101740 A101741

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Extensions

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

a(17)-a(19) from Kamada data by Ray Chandler, May 01 2015

a(20)-a(21) from Robert Price, May 30 2015

Status

approved