A101840 Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) - 3 for n > 0.

0, 1, 11, 14, 50, 193, 497, 2135, 2821, 3761, 7427, 22739, 30451, 37951, 55253

Offset

1,3

Comments

Numbers n such that (330*10^n + 3)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 6 followed by digit 7 is prime.

Numbers corresponding to terms <= 497 are certified primes.

a(16) > 10^5. - Robert Price, Jan 29 2015

All terms except the first are congruent to 1, 2 or 5 (mod 6), since 37 | A(3n) and 7 | A(6n+4). - Robert Israel, Dec 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..15.

Makoto Kamada, Prime numbers of the form 366...667.

Index entries for primes involving repunits.

Formula

a(n) = A102975(n) - 1.

Example

367 is prime, hence 1 is a term.
3666666666667 is prime, hence 11 is a term.

Maple

select(t -> isprime((330*(10^t)+3)/9), [0, seq(seq(6*i+j, j=[1, 2, 5]), i=0..1000)]); # Robert Israel, Dec 02 2015

Mathematica

A101840[n_] := If[PrimeQ[((330*(10^n)) + 3)*(1/9)] == True, n, 0];
DeleteDuplicates[Table[A101840[n], {n, 0, 55300}]] (* Abdul Gaffar Khan, Nov 29 2015 *)

Prog

(PARI) a=37; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-3)
(PARI) for(n=0, 1500, if(isprime((330*10^n+3)/9), print1(n, ", ")))
(Magma) [n: n in [0..500] | IsPrime((330*10^n+3) div 9)]; // Vincenzo Librandi, Nov 30 2015

Crossrefs

Cf. A000533, A002275, A102975.

Sequence in context: A371072 A371073 A344842 * A061087 A063964 A349224

Adjacent sequences: A101837 A101838 A101839 * A101841 A101842 A101843

Keyword

nonn,hard,more

Author

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

Extensions

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

a(12)-a(15) derived from A102975 by Robert Price, Jan 29 2015

Status

approved