A101572 Indices of primes in sequence defined by A(0) = 59, A(n) = 10*A(n-1) - 71 for n > 0.

0, 2, 6, 14, 21, 188, 444, 542, 632, 756, 8724, 9002, 37401

Offset

1,2

Comments

Numbers n such that (460*10^n + 71)/9 is prime.

Numbers n such that digit 5 followed by n >= 0 occurrences of digit 1 followed by digit 9 is prime.

Numbers corresponding to terms <= 756 are certified primes.

a(14) > 10^5. - Robert Price, Jul 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..13.

Makoto Kamada, Prime numbers of the form 511...119.

Index entries for primes involving repunits.

Formula

a(n) = A103007(n+1) - 1.

Example

59 is prime, hence 0 is a term.

Maple

map(`-`, [ListTools:-SearchAll(true,
[seq(isprime((460*10^n+71)/9), n=0..2000)])], 1); # Robert Israel, Jul 13 2015

Mathematica

a[0] = 59; a[n_] := a[n] = 10 a[n - 1] - 71; Flatten@ Position[Table[a@ n, {n, 0, 1000}], _Integer?PrimeQ] - 1 (* Michael De Vlieger, Jul 13 2015 *)

Prog

(PARI) a=59; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-71)
(PARI) for(n=0, 1500, if(isprime((460*10^n+71)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103007.

Sequence in context: A009218 A071122 A173724 * A080766 A262506 A228649

Adjacent sequences: A101569 A101570 A101571 * A101573 A101574 A101575

Keyword

nonn,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 09 2004

Extensions

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

a(13) from Erik Branger May 01 2013 by Ray Chandler, Apr 30 2015

Status

approved