A101721 Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 43 for n > 0.

0, 3, 135, 180, 324, 3291, 3870, 4689, 7875, 11910, 16095, 21648, 43044

Offset

1,2

Comments

Numbers n such that (380*10^n + 43)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 2 followed by digit 7 is prime.

Numbers corresponding to terms <= 324 are certified primes.

a(14) > 10^5. - Robert Price, May 08 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 422...227.

Index entries for primes involving repunits.

Formula

a(n) = A102986(n) - 1.

Example

42227 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 300], PrimeQ[(380*10^# + 43)/9] &] (* Robert Price, May 08 2015 *)

Prog

(PARI) a=47; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-43)
(PARI) for(n=0, 1500, if(isprime((380*10^n+43)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102986.

Sequence in context: A157086 A366306 A051376 * A173582 A065973 A110973

Adjacent sequences: A101718 A101719 A101720 * A101722 A101723 A101724

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Extensions

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

a(10)-a(13) from Kamada data by Ray Chandler, Apr 30 2015

Status

approved