A101011 Indices of primes in sequence defined by A(0) = 97, A(n) = 10*A(n-1) - 13 for n > 0.

0, 6, 66, 126, 2106, 10002, 13740, 41522

Offset

1,2

Comments

Numbers n such that (860*10^n + 13)/9 is prime.

Numbers n such that digit 9 followed by n >= 0 occurrences of digit 5 followed by digit 7 is prime.

Numbers corresponding to terms <= 126 are certified primes.

a(9) > 10^5. - Robert Price, Nov 10 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..8.

Makoto Kamada, Prime numbers of the form 955...557.

Index entries for primes involving repunits.

Formula

a(n) = A103102(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008; adjusted by Robert Price, Nov 10 2015

Example

95555557 is prime, hence 6 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(860*10^# + 13)/9] &] (* Robert Price, Nov 10 2015 *)

Prog

(PARI) a=97; for(n=0, 2200, if(isprime(a), print1(n, ", ")); a=10*a-13)
(PARI) for(n=0, 2200, if(isprime((860*10^n+13)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103102.

Sequence in context: A119144 A153087 A117794 * A292456 A292736 A119140

Adjacent sequences: A101008 A101009 A101010 * A101012 A101013 A101014

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Extensions

a(6)-a(8) from Kamada data by Ray Chandler, Apr 28 2015

Corrected Formula to adjust for change in A103102 by Robert Price, Nov 10 2015

Status

approved