A101715 Indices of primes in sequence defined by A(0) = 49, A(n) = 10*A(n-1) - 81 for n > 0.

1, 3, 4, 7, 8, 27, 190, 195, 2037, 34413, 39265, 50578, 94285, 108411, 130479, 178090, 185354

Offset

1,2

Comments

Numbers n such that 40*10^n + 9 is prime.

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

Numbers corresponding to terms <= 195 are certified primes.

a(18) > 2*10^5. - Robert Price, May 24 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..17.

Makoto Kamada, Prime numbers of the form 400...009.

Formula

a(n) = A101394(n+1) - 1.

Example

40009 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 1000], PrimeQ[40*10^# + 9] &] (* Robert Price, May 24 2015 *)

Prog

(PARI) a=49; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-81)
(PARI) for(n=0, 1500, if(isprime(40*10^n+9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A101394.

Sequence in context: A214096 A169943 A215110 * A249751 A169893 A169899

Adjacent sequences: A101712 A101713 A101714 * A101716 A101717 A101718

Keyword

nonn,hard,more

Author

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

Extensions

2037 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(10)-a(11) from Kamada data by Ray Chandler, Apr 30 2015

a(12)-a(17) from Robert Price, May 24 2015

Status

approved