A101007 Indices of primes in sequence defined by A(0) = 93, A(n) = 10*A(n-1) + 13 for n > 0.

29, 40, 227, 580, 1289, 2579, 3695, 11389, 21557

Offset

1,1

Comments

Numbers n such that (850*10^n - 13)/9 is prime.

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

Numbers corresponding to terms <= 580 are certified primes.

a(10) > 10^5. - Robert Price, Nov 05 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..9.

Makoto Kamada, Prime numbers of the form 944...443.

Index entries for primes involving repunits.

Formula

a(n) = A103098(n) - 1.

Example

9444444444444444444444444444443 is prime, hence 29 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(850*10^# - 13)/9] &] (* Robert Price, Nov 05 2015 *)

Prog

(PARI) a=93; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+13)
(PARI) for(n=0, 1500, if(isprime((850*10^n-13)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103098.

Sequence in context: A159888 A108325 A242555 * A253252 A155575 A229059

Adjacent sequences: A101004 A101005 A101006 * A101008 A101009 A101010

Keyword

nonn,hard,more,less

Author

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

Extensions

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

a(8)-a(9) from Kamada data by Ray Chandler, Apr 28 2015

Status

approved