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

Author

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

Keywords

• nonn
• hard
• more

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.

Examples

			4001 is prime, hence 2 is a term.
		

References

• Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

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

Crossrefs

Cf. A000533, A002275, A056806.

Programs

Mathematica

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

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,",")))

Formula

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

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