A102014 Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 51 for n > 0.

0, 1, 3, 6, 9, 12, 13, 21, 22, 28, 37, 49, 52, 66, 103, 349, 375, 411, 1204, 1834, 2509, 2667, 6096, 8295, 14295, 43368, 127348, 142033

Offset

1,3

Comments

Numbers n such that (120*10^n + 51)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 3 followed by digit 9 is prime.

Numbers corresponding to terms <= 411 are certified primes.

a(27) > 10^5. - Robert Price, Nov 15 2014

a(29) > 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..28.

Makoto Kamada, Prime numbers of the form 133...339.

Index entries for primes involving repunits.

Formula

a(n) = A102933(n) - 1. - Robert Price, Nov 15 2014

Example

139 is prime, hence 1 is a term.

Maple

A102014:=n->`if`(isprime((120*10^n + 51)/9), n, NULL): seq(A102014(n), n=0..1000); # Wesley Ivan Hurt, Nov 15 2014

Prog

(PARI) a=19; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-51)
(PARI) for(n=0, 1500, if(isprime((120*10^n+51)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102933.

Sequence in context: A092452 A230215 A120688 * A337091 A168045 A288522

Adjacent sequences: A102011 A102012 A102013 * A102015 A102016 A102017

Keyword

nonn,hard,more

Author

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

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(25)-a(26) derived from A102933 by Robert Price, Nov 15 2014

a(27)-a(28) from Tyler Busby, Feb 01 2023

Status

approved