cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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

Examples

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

References

  • Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Crossrefs

Programs

  • Magma
    [n: n in [0..500] | IsPrime((330*10^n+3) div 9)]; // Vincenzo Librandi, Nov 30 2015
  • 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 *)
  • 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,",")))
    

Formula

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

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

A294396 Numbers k such that 12*10^k + 1 is prime.

Original entry on oeis.org

0, 2, 38, 80, 9230, 25598, 39500
Offset: 1

Views

Author

Patrick A. Thomas, Feb 12 2018

Keywords

Comments

k must be even since 12*10^k + 1 is divisible by 11 if k is odd. - Robert G. Wilson v, Feb 12 2018
a(7) > 27440. - Robert G. Wilson v, Feb 17 2018
a(8) > 10^5. - Jeppe Stig Nielsen, Jan 31 2023

Examples

			13 and 1201 are prime, so 0 and 2 are the initial values.
		

Crossrefs

Programs

  • Mathematica
    ParallelMap[ If[ PrimeQ[12*10^# +1], #, Nothing] &, 2 + 6Range@ 4500] (* Robert G. Wilson v, Feb 13 2018 *)
  • PARI
    isok(k) = isprime(12*10^k + 1); \\ Altug Alkan, Mar 04 2018

Extensions

a(5) from Robert G. Wilson v, Feb 12 2018
a(6) from Robert G. Wilson v, Feb 13 2018
a(7) from Jeppe Stig Nielsen, Jan 28 2023
Showing 1-2 of 2 results.