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

Author

Amarnath Murthy, Jan 02 2006

Keywords

• base
• nonn
• less

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.

Examples

			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)
		

Crossrefs

Subsequence of A090155 and hence A235154.

Programs

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 *)

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