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

1,2

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

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 244...443.

Index entries for primes involving repunits.

Formula

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

Example

24443 is prime, hence 3 is a term.

Prog

(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, ", ")))

Crossrefs

Cf. A000533, A002275, A102953.

Sequence in context: A221182 A109781 A360888 * A153982 A119367 A079801

Adjacent sequences: A101955 A101956 A101957 * A101959 A101960 A101961

Keyword

nonn,hard,more

Author

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

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

Status

approved