A101518 Indices of primes in sequence defined by A(0) = 67, A(n) = 10*A(n-1) - 63 for n > 0.

0, 1, 2, 7, 8, 18, 57, 120, 186, 805, 854, 1018, 2592, 2748, 3015, 4294, 9663, 14926, 34561, 64386, 71298, 71950

Offset

1,3

Comments

Numbers n such that 60*10^n + 7 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 0 followed by digit 7 is prime.

Numbers corresponding to terms <= 854 are certified primes.

a(23) > 2*10^5. - Robert Price, Sep 17 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..22.

Makoto Kamada, Prime numbers of the form 600...007.

Formula

a(n) = A103026(n-1) - 1.

Example

6007 is prime, hence 2 is a term.

Mathematica

For[n=1, n<=3000, n++, If[PrimeQ[60*10^n+7], Print[n]]] (Steinerberger)

Prog

(PARI) a=67; for(n=0, 1200, if(isprime(a), print1(n, ", ")); a=10*a-63)
(PARI) for(n=0, 1200, if(isprime(60*10^n+7), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103026.

Sequence in context: A300476 A213037 A287343 * A055247 A015617 A306903

Adjacent sequences: A101515 A101516 A101517 * A101519 A101520 A101521

Keyword

nonn,hard

Author

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

Extensions

a(13)-a(15) from Stefan Steinerberger, Feb 03 2006

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

a(18)-a(22) from Kamada link by Ray Chandler, Apr 30 2015

Status

approved