A101739 Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 63 for n > 0.

0, 2, 3, 7, 13, 15, 23, 60, 79, 86, 103, 107, 143, 2156, 3324, 4121, 20717, 51162, 140743

Offset

1,2

Comments

Numbers n such that (450*10^n - 63)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

Numbers corresponding to terms <= 143 are certified primes.

a(20) > 2*10^5. - Robert Price, Sep 15 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..19.

Makoto Kamada, Prime numbers of the form 499...993.

Index entries for primes involving repunits.

Formula

a(n) = A103002(n) - 1.

Example

4993 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(450*10^# - 63)/9] &] (* Robert Price, Sep 15 2015 *)

Prog

(PARI) a=43; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+63)
(PARI) for(n=0, 1500, if(isprime((450*10^n-63)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A108837, A103002.

Sequence in context: A318401 A322703 A225098 * A363450 A336378 A141633

Adjacent sequences: A101736 A101737 A101738 * A101740 A101741 A101742

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 01 2008

a(17)-a(18) from Kamada data by Ray Chandler, May 01 2015

a(19) from Robert Price, Sep 15 2015

Status

approved