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 1-6 of 6 results.

A141470 Number of 3's in A139067(n).

Original entry on oeis.org

0, 1, 1, 1, 2, 3, 4, 3, 1, 7, 1, 4, 6, 7, 10, 7, 16, 5, 9, 11, 3, 22, 5, 17, 14, 12, 7, 21, 20, 1, 25, 9, 21, 7, 4, 22, 13, 14, 18, 33, 35, 20, 13, 53, 51, 19, 7, 46, 52, 3, 5, 9, 12, 42, 12, 17, 34, 22, 55, 51, 57, 31, 3, 71, 41, 7, 55, 64, 5, 63, 37, 41, 31, 91, 61, 69, 1
Offset: 1

Views

Author

Paul Curtz and Ray Chandler, Aug 14 2008

Keywords

Crossrefs

Cf. A139067.

A141471 Number of 2's in A139067(n).

Original entry on oeis.org

1, 0, 1, 2, 1, 1, 1, 4, 7, 2, 10, 7, 5, 4, 1, 5, 1, 14, 10, 8, 19, 1, 19, 8, 13, 17, 23, 10, 13, 35, 11, 28, 16, 31, 37, 19, 32, 31, 29, 14, 13, 31, 40, 1, 4, 37, 50, 11, 5, 55, 53, 50, 47, 17, 49, 47, 35, 49, 16, 22, 16, 44, 73, 5, 38, 76, 31, 23, 83, 25, 53, 50, 61, 1
Offset: 1

Views

Author

Paul Curtz and Ray Chandler, Aug 14 2008

Keywords

Crossrefs

Cf. A139067.

A141472 Number of digits in A139067(n).

Original entry on oeis.org

1, 1, 2, 3, 3, 4, 5, 7, 8, 9, 11, 11, 11, 11, 11, 12, 17, 19, 19, 19, 22, 23, 24, 25, 27, 29, 30, 31, 33, 36, 36, 37, 37, 38, 41, 41, 45, 45, 47, 47, 48, 51, 53, 54, 55, 56, 57, 57, 57, 58, 58, 59, 59, 59, 61, 64, 69, 71, 71, 73, 73, 75, 76, 76, 79, 83, 86, 87, 88
Offset: 1

Views

Author

Paul Curtz and Ray Chandler, Aug 14 2008

Keywords

Crossrefs

Cf. A139067.

A020458 Primes that contain digits 2 and 3 only.

Original entry on oeis.org

2, 3, 23, 223, 233, 2333, 3323, 23333, 32233, 32323, 33223, 222323, 232333, 233323, 323233, 323333, 333233, 333323, 2222333, 2223233, 2232323, 2233223, 2332333, 2333323, 3222223, 3223223, 3223333, 3233323, 3233333, 3332233, 3333233, 22222223, 22223323, 22232233
Offset: 1

Views

Author

Keywords

Crossrefs

Programs

  • Mathematica
    Flatten[Table[Select[FromDigits/@Tuples[{2,3},n],PrimeQ],{n,7}]] (* Harvey P. Dale, Jul 13 2012 *)
  • PARI
    go(n)=my(v=List([2]),x,t); for(d=1,n, x=10^d\9*2; forstep(i=1,2^d-1,2, if(ispseudoprime(t=x+fromdigits(binary(i))), listput(v,t)))); Vec(v) \\ Charles R Greathouse IV, Sep 14 2015
    
  • Python
    from sympy import isprime
    from itertools import count, islice, product
    def agen(): # generator of terms
        yield from [2, 3]
        for d in count(2):
            for first in product("23", repeat=d-1):
                t = int("".join(first) + "3")
                if isprime(t): yield t
    print(list(islice(agen(), 34))) # Michael S. Branicky, Jun 08 2022

Extensions

Edited by N. J. A. Sloane, Jul 27 2008 at the suggestion of Dmitry Kamenetsky.
Edited by Charles R Greathouse IV, Mar 17 2010

A151913 Numbers n for which (8+n!)/8 is prime.

Original entry on oeis.org

7, 9, 10, 12, 14, 20, 23, 24, 29, 44, 108, 2049, 3072, 4862, 8807, 15089
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

a(17) > 25000. - Robert Price, Dec 20 2016

Crossrefs

For primes of the form (8+k!!)/8 see A139066.
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 8)/8], AppendTo[a, n]], {n, 1, 500}]; a
  • PARI
    is(n)=n>6 && isprime((8+n!)/8) \\ Charles R Greathouse IV, Apr 29 2016

Extensions

Definition corrected Feb 24 2010
More terms from Serge Batalov, Feb 18 2015
a(15)-a(16) from Robert Price, Dec 20 2016

A157733 a(0)=2, a(1)=3. Then 2 or 22 followed by a string of 3's such that the sum of the digits of a(n) is equal to prime(n).

Original entry on oeis.org

2, 3, 23, 223, 2333, 22333, 233333, 2233333, 23333333, 2333333333, 22333333333, 2233333333333, 23333333333333, 223333333333333, 2333333333333333, 233333333333333333, 23333333333333333333, 223333333333333333333
Offset: 0

Views

Author

Paul Curtz, Mar 05 2009

Keywords

Comments

We search for w twos and t threes in prime(n) = 2*w + 3*t. If t = floor(prime(n)/3) would lead to w = 1/2, we decrease t by 1.
The number of twos is 3 - A039701(n) if n > 1.
If prime(n) is congruent to 1 mod 6, then a(n) starts with 22, but if prime(n) is congruent to 5 mod 6, then a(n) starts with 2. - Alonso del Arte, Dec 04 2013

Examples

			a(3) = 23 because the third prime is 5 and 2 + 3 = 5.
a(4) = 223 because the fourth prime is 7 and 2 + 2 + 3 = 7.
a(5) = 2333 because the fifth prime is 11 and 2 + 3 + 3 + 3 = 11.
		

Crossrefs

Programs

  • Mathematica
    Module[{nn = 30, t1, t2}, t1 = FromDigits/@Select[Table[PadRight[{2}, n, 3], {n, 2, nn}], PrimeQ[Total[#]] &]; t2 = FromDigits/@ Select[ Table[ PadRight[{2, 2}, n, 3], {n, 2, nn}], PrimeQ[Total[#]] &]; Union[ Join[ {2, 3}, t1, t2]]] (* Harvey P. Dale, Mar 06 2013 *)

Extensions

Edited by R. J. Mathar, Mar 15 2009
Showing 1-6 of 6 results.