cp's OEIS Frontend

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.

%I A112750 #31 Dec 11 2024 15:32:28
%S A112750 71,733,7333,79999,733333,71111111,799999999,79999999999,
%T A112750 79999999999999999999999999,
%U A112750 79999999999999999999999999999999999999999999999999,733333333333333333333333333333333333333333333333333333,71111111111111111111111111111111111111111111111111111111
%N 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.
%C A112750 For all j > 0, k must be 1, 3, or 9, since a number with --
%C A112750 -- digits 7kk...kk where k is even will be a proper multiple of 2;
%C A112750 -- digits 755...55 will be a proper multiple of 5; and
%C A112750 -- digits 777...77 will be a proper multiple of 7.
%e A112750 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.
%e A112750 From _Jon E. Schoenfield_, Feb 23 2021:  (Start)
%e A112750 Terms begin as follows:
%e A112750    n   j  k  a(n)
%e A112750   --  --  -  --------------------------------------------------------
%e A112750    1   1  1  71
%e A112750    2   2  3  733
%e A112750    3   3  3  7333
%e A112750    4   4  9  79999
%e A112750    5   5  3  733333
%e A112750    -   6  - (7111111, 7333333, 7999999 are composite)
%e A112750    6   7  1  71111111
%e A112750    7   8  9  799999999
%e A112750    -   9  - (7111111111, 7333333333, 7999999999 are composite)
%e A112750    8  10  9  79999999999
%e A112750    -  11  - (711111111111, 733333333333, 799999999999 are composite)
%e A112750    -  12  - (all composite)
%e A112750    -  13  - (all composite)
%e A112750       ...
%e A112750    9  25  9  79999999999999999999999999
%e A112750       ...
%e A112750   10  49  9  79999999999999999999999999999999999999999999999999
%e A112750       ...
%e A112750   11  53  3  733333333333333333333333333333333333333333333333333333
%e A112750   12  55  1  71111111111111111111111111111111111111111111111111111111
%e A112750 (End)
%t A112750 SelectFirst[#,PrimeQ]&/@Table[FromDigits[PadRight[{7},n,p]],{n,2,60},{p,{1,3,9}}]/.Missing["NotFound"]->Nothing (* _Harvey P. Dale_, Apr 19 2021 *)
%Y A112750 Subsequence of A090155 and hence A235154.
%K A112750 base,nonn,less
%O A112750 1,1
%A A112750 _Amarnath Murthy_, Jan 02 2006
%E A112750 More terms added by _Harvey P. Dale_, Jan 24 2010
%E A112750 Name corrected (using a suggestion from _Felix Fröhlich_) and Example edited by _Jon E. Schoenfield_, May 28 2019
%E A112750 Terms corrected by _Jon E. Schoenfield_, Feb 23 2021