A101529 Indices of primes in sequence defined by A(0) = 67, A(n) = 10*A(n-1) - 23 for n > 0.

0, 1, 4, 9, 39, 46, 57, 72, 91, 112, 123, 129, 886, 1233, 1537, 2062, 2590, 2785, 3144, 21687, 32380, 39169, 47790, 83877

Offset

1,3

Comments

Numbers n such that (580*10^n + 23)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 4 followed by digit 7 is prime.

Numbers corresponding to terms <= 886 are certified primes.

a(25) > 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..24.

Makoto Kamada, Prime numbers of the form 644...447.

Index entries for primes involving repunits.

Formula

a(n) = A103036(n) - 1.

Example

647 is prime, hence 1 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(580*10^# + 23)/9] &] (* Robert Price, Sep 15 2015 *)

Prog

(PARI) a=67; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-23)
(PARI) for(n=0, 1500, if(isprime((580*10^n+23)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103036.

Sequence in context: A149151 A149152 A149153 * A149154 A149155 A149156

Adjacent sequences: A101526 A101527 A101528 * A101530 A101531 A101532

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(20)-a(23) from Kamada data by Ray Chandler, Apr 30 2015

a(24) from Robert Price, Sep 15 2015

Status

approved