A101958 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) + 13 for n > 0.

0, 3, 6, 11, 29, 93, 177, 195, 563, 1800, 3519, 3537, 8232, 35160, 37404, 42329, 70050, 90791

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (220*10^n - 13)/9 is prime.

Numbers n such that digit 2 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.

Numbers corresponding to terms <= 563 are certified primes.

With changed signs, expansion of sinh(atan(x)).

Next term after 3537 is greater than 5000. - Ryan Propper, Jun 16 2005

a(19) > 10^5. - Robert Price, Mar 16 2015

Examples

			24443 is prime, hence 3 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 244...443.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A102953.

Programs

PARI

a=23;for(n=0,2000,if(isprime(a),print1(n,","));a=10*a+13)

PARI

for(n=0,2000,if(isprime((220*10^n-13)/9),print1(n,",")))

Formula

a(n) = A102953(n) - 1.

Extensions

2 more terms from Ryan Propper, Jun 16 2005

8232 from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007

a(14)-a(18) derived from A102953 by Robert Price, Mar 16 2015