A112750 Smallest prime of the form 7 followed by j copies of the digit k, where j runs through those positive values for which such a prime exists.

71, 733, 7333, 79999, 733333, 71111111, 799999999, 79999999999, 79999999999999999999999999, 79999999999999999999999999999999999999999999999999, 733333333333333333333333333333333333333333333333333333, 71111111111111111111111111111111111111111111111111111111

Offset

1,1

Comments

For all j > 0, k must be 1, 3, or 9, since a number with --

-- digits 7kk...kk where k is even will be a proper multiple of 2;

-- digits 755...55 will be a proper multiple of 5; and

-- digits 777...77 will be a proper multiple of 7.

Links

Table of n, a(n) for n=1..12.

Example

7333 is a term because it is prime and is 7 followed by three copies of 3, and the numbers 7000, 7111, and 7222 are all nonprime.
From Jon E. Schoenfield, Feb 23 2021:  (Start)
Terms begin as follows:
   n   j  k  a(n)
  --  --  -  --------------------------------------------------------
   1   1  1  71
   2   2  3  733
   3   3  3  7333
   4   4  9  79999
   5   5  3  733333
   -   6  - (7111111, 7333333, 7999999 are composite)
   6   7  1  71111111
   7   8  9  799999999
   -   9  - (7111111111, 7333333333, 7999999999 are composite)
   8  10  9  79999999999
   -  11  - (711111111111, 733333333333, 799999999999 are composite)
   -  12  - (all composite)
   -  13  - (all composite)
      ...
   9  25  9  79999999999999999999999999
      ...
  10  49  9  79999999999999999999999999999999999999999999999999
      ...
  11  53  3  733333333333333333333333333333333333333333333333333333
  12  55  1  71111111111111111111111111111111111111111111111111111111
(End)

Mathematica

SelectFirst[#, PrimeQ]&/@Table[FromDigits[PadRight[{7}, n, p]], {n, 2, 60}, {p, {1, 3, 9}}]/.Missing["NotFound"]->Nothing (* Harvey P. Dale, Apr 19 2021 *)

Crossrefs

Subset of A090155.

Sequence in context: A180327 A201039 A142674 * A351896 A089706 A220623

Adjacent sequences: A112747 A112748 A112749 * A112751 A112752 A112753

Keyword

base,nonn,less

Author

Amarnath Murthy, Jan 02 2006

Extensions

More terms added by Harvey P. Dale, Jan 24 2010

Name corrected (using a suggestion from Felix Fröhlich) and Example edited by Jon E. Schoenfield, May 28 2019

Terms corrected by Jon E. Schoenfield, Feb 23 2021

Status

approved