A102009 Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) - 7 for n > 0.

0, 2, 8, 47, 57, 152, 260, 875, 1178, 1595, 17714, 63717

Offset

1,2

Comments

Numbers n such that (110*10^n + 7)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 2 followed by digit 3 is prime.

Numbers corresponding to terms <= 875 are certified primes.

a(13) > 10^5. - Robert Price, Nov 15 2014

a(13) > 2*10^5. - Tyler Busby, Feb 01 2023

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..12.

Makoto Kamada, Prime numbers of the form 122...223.

Index entries for primes involving repunits

Formula

a(n) = A102929(n+1) - 1. - Robert Price, Nov 15 2014

Example

1223 is prime, hence 2 is a term.

Prog

(PARI) a=13; for(n=0, 1600, if(isprime(a), print1(n, ", ")); a=10*a-7)
(PARI) for(n=0, 1600, if(isprime((110*10^n+7)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102929.

Sequence in context: A246386 A096656 A297014 * A254747 A298698 A354498

Adjacent sequences: A102006 A102007 A102008 * A102010 A102011 A102012

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Extensions

a(11)-a(12) derived from A102929 by Robert Price, Nov 15 2014

Status

approved