A101534 Indices of primes in sequence defined by A(0) = 69, A(n) = 10*A(n-1) - 31 for n > 0.

1, 4, 7, 16, 19, 64, 82, 89, 107, 251, 334, 1487, 6355, 65711, 96797

Offset

1,2

Comments

Numbers n such that (590*10^n + 31)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 5 followed by digit 9 is prime.

Numbers corresponding to terms <= 334 are certified primes.

Next term, if it exists, is bigger than 3000. - Stefan Steinerberger, Feb 03 2006

a(16) > 10^5. - Robert Price, Sep 13 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..15.

Makoto Kamada, Prime numbers of the form 655...559.

Index entries for primes involving repunits.

Formula

a(n) = A103041(n) - 1.

Example

655559 is prime, hence 4 is a term.

Mathematica

For[n=1, n<= 3000, n++, If[PrimeQ[(590*10^n + 31)/9], Print[n]]] (Steinerberger)

Prog

(PARI) a=69; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-31)
(PARI) for(n=0, 1500, if(isprime((590*10^n+31)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103041.

Sequence in context: A353259 A345429 A256926 * A110933 A299423 A067398

Adjacent sequences: A101531 A101532 A101533 * A101535 A101536 A101537

Keyword

nonn,hard,more

Author

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

Extensions

More terms from Stefan Steinerberger, Feb 03 2006

6355 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(14)-a(15) from Robert Price, Sep 13 2015

Status

approved