A101712 Indices of primes in sequence defined by A(0) = 41, A(n) = 10*A(n-1) - 9 for n > 0.

0, 1, 2, 12, 228, 241, 308, 956, 1472, 1493, 3181, 3726, 4176, 23209, 25718, 32834, 36989, 103957

Offset

1,3

Comments

Numbers n such that 40*10^n + 1 is prime.

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

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..18.

Makoto Kamada, Prime numbers of the form 400...001.

Formula

a(n) = A056806(n+1) - 1.

Example

4001 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 1500], PrimeQ[4*10^# + 1] &] (* Robert Price, Mar 19 2015 *)

Prog

(PARI) a=41; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-9)
(PARI) for(n=0, 1500, if(isprime(40*10^n+1), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A056806.

Sequence in context: A132879 A377642 A348332 * A156484 A333447 A347597

Adjacent sequences: A101709 A101710 A101711 * A101713 A101714 A101715

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 02 2008

Added missing term a(16)=32834 by Robert Price, Mar 19 2015

Status

approved