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 1-4 of 4 results.

A065584 Smallest prime beginning with exactly n 1's.

Original entry on oeis.org

2, 13, 11, 1117, 11113, 111119, 11111101, 11111117, 111111113, 11111111129, 11111111113, 1111111111139, 11111111111123, 1111111111111013, 1111111111111123, 11111111111111101, 11111111111111119
Offset: 0

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Author

Robert G. Wilson v, Nov 28 2001

Keywords

Comments

Largest terms are only probable primes. Some terms of the sequence are also in A004022 (repunit primes) or A056710 (all digits same except last digit). All terms of A004022 are in the current sequence.
According to the Magma Calculator (at http://magma.maths.usyd.edu.au/calc/), all 201 terms in the table (and thus all 17 terms listed above) are, in fact, prime. - Jon E. Schoenfield, Aug 24 2009

Crossrefs

Cf. A004022 (repunit primes), A056710 (near-repdigit primes).

Extensions

Corrected by Don Reble, Jan 17 2007
Offset corrected by Sean A. Irvine, Sep 06 2023

A068104 Smallest prime starting with n 3s.

Original entry on oeis.org

2, 3, 331, 3331, 33331, 333331, 3333331, 33333331, 3333333319, 33333333329, 333333333323, 3333333333301, 33333333333319, 333333333333307, 3333333333333301, 33333333333333323, 333333333333333331
Offset: 0

Views

Author

Amarnath Murthy, Feb 20 2002

Keywords

Crossrefs

Programs

  • Mathematica
    Join[{2,3},Table[SelectFirst[Join[10FromDigits[PadRight[{},k,3]]+{1,7,9},Flatten[Table[100 FromDigits[PadRight[{},k,3]]+10n+{1,3,7,9},{n,0,9}]],Flatten[Table[1000 FromDigits[PadRight[{},k,3]]+100n+{1,3,7,9},{n,0,99}]]],PrimeQ],{k,2,20}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 01 2019 *)

Extensions

More terms from Sascha Kurz, Mar 19 2002

A068103 Smallest prime starting with at least n 2s.

Original entry on oeis.org

2, 2, 223, 2221, 22229, 2222203, 22222223, 22222223, 222222227, 22222222223, 22222222223, 2222222222243, 22222222222201, 22222222222229, 222222222222227, 222222222222222043, 222222222222222221
Offset: 0

Views

Author

Amarnath Murthy, Feb 20 2002

Keywords

Crossrefs

Programs

  • PARI
    A068103(n)={n=10^n\9*2;n>2&for(d=1,9e9,n*=10;for(t=1,10^d-1,ispseudoprime(n+t)&return(n+t)));2} \\ - M. F. Hasler, Oct 17 2012

Extensions

More terms from Sascha Kurz, Mar 19 2002
Corrected by Don Reble, Jan 17 2007

A065588 Smallest prime beginning with exactly n 5's.

Original entry on oeis.org

2, 5, 557, 5557, 555521, 555557, 55555517, 55555553, 5555555501, 5555555557, 5555555555057, 555555555551, 5555555555551, 555555555555529, 555555555555557, 55555555555555519, 5555555555555555021, 555555555555555559, 55555555555555555567, 5555555555555555555087
Offset: 0

Views

Author

Robert G. Wilson v, Nov 28 2001

Keywords

Crossrefs

Cf. A037063, A065584 - A065592. Different from A068105.

Programs

  • Python
    from sympy import isprime
    def a(n):
      if n < 2: return list([2, 5])[n]
      n5s, i, pow10, end_digits = int('5'*n), 1, 1, 0
      while True:
        i = 1
        while i < pow10:
          istr = str(i)
          if istr[0] == '5' and len(istr) == end_digits:
            i += 2 if pow10 <= 10 else pow10 // 10
          else:
            t = n5s * pow10 + i
            if isprime(t): return t
            i += 2
        pow10 *= 10; end_digits += 1
    print([a(n) for n in range(20)]) # Michael S. Branicky, Feb 05 2021, corrected Mar 03 2021

Extensions

Corrected by N. J. A. Sloane, Jan 11 2007 and by Don Reble, Jan 17 2007
Offset corrected by Michael S. Branicky, Feb 05 2021
Showing 1-4 of 4 results.