A101849 Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) + 27 for n > 0.

0, 1, 13, 19, 29, 43, 65, 259, 871, 8845, 26743, 57505, 98471, 106891

Offset

1,3

Comments

Numbers n such that (360*10^n - 27)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 9 followed by digit 7 is prime.

Numbers corresponding to terms <= 871 are certified primes.

a(14) > 10^5. - Robert Price, Mar 17 2015.

a(15) > 2*10^5. - Robert Price, Oct 02 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..14.

Makoto Kamada, Prime numbers of the form 399...997.

Index entries for primes involving repunits.

Formula

a(n) = A101398(n) - 1.

Example

397 is prime, hence 1 is a term.

Mathematica

Select[Range[0, 1000], PrimeQ[(360*10^# - 27)/9] &] (* Robert Price, Mar 17 2015 *)

Prog

(PARI) a=37; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+27)
(PARI) for(n=0, 1500, if(isprime((360*10^n-27)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A101155, A169830, A101398.

Sequence in context: A038954 A005106 A120140 * A141562 A353205 A108097

Adjacent sequences: A101846 A101847 A101848 * A101850 A101851 A101852

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004

Extensions

8845 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(11)-a(13) derived from A101398 by Robert Price, Mar 17 2015

a(14) from Robert Price, Oct 02 2015

Status

approved