A101835 Indices of primes in sequence defined by A(0) = 31, A(n) = 10*A(n-1) + 41 for n > 0.

0, 5, 8, 14, 23, 47, 72, 74, 96, 248, 272, 2487, 14498, 74772, 87448

Offset

1,2

Comments

Numbers n such that (320*10^n - 41)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 5 followed by digit 1 is prime.

Numbers corresponding to terms <= 272 are certified primes.

a(16) > 10^5. - Robert Price, May 24 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 355...551.

Index entries for primes involving repunits.

Formula

a(n) = A102971(n) - 1.

Example

3555555551 is prime, hence 8 is a term.

Mathematica

#-1&/@Flatten[Position[NestList[10#+41&, 31, 280], _?PrimeQ]] (* Harvey P. Dale, Jul 17 2011 *)
Select[Range[0, 10000], PrimeQ[(320 10^# - 41)/9] &] (* Vincenzo Librandi, May 25 2015 *)

Prog

(PARI) a=31; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+41)
(PARI) for(n=0, 1500, if(isprime((320*10^n-41)/9), print1(n, ", ")))
(Magma) [n: n in [0..2000] | IsPrime((320*10^n-41) div 9)]; // Vincenzo Librandi, May 26 2015

Crossrefs

Cf. A000533, A002275, A102971.

Sequence in context: A092590 A065394 A124011 * A192522 A133641 A164094

Adjacent sequences: A101832 A101833 A101834 * A101836 A101837 A101838

Keyword

nonn,hard,more

Author

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

Extensions

2487 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(13) from Kamada data by Ray Chandler, May 01 2015

a(14)-a(15) from Robert Price, May 24 2015

Status

approved