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Smallest prime obtained by appending 3's to k, where k runs through the numbers not divisible by 3, or -1 if no such prime exists.
3

%I #43 Jun 20 2024 02:42:25

%S 13,23,43,53,73,83,103,113,1333333333333333,1433,163,173,193,20333,

%T 223,233,2533333333,263,283,293,313,323333,3433,353,373,383

%N Smallest prime obtained by appending 3's to k, where k runs through the numbers not divisible by 3, or -1 if no such prime exists.

%C Next term is 40 followed by 483 3's, and is too large to display here (see the b-file).

%H Toshitaka Suzuki, <a href="/A112394/b112394.txt">Table of n, a(n) for n = 1..273</a> (terms 1..200 from Harvey P. Dale)

%e For k = 1, we get the prime 13.

%e For k = 13, we get the prime 1333333333333333 (the smaller numbers 133,1333,13333 etc. are not primes).

%e For k = 4070 and 9287, no such prime exists, so we get -1 for the value. Compare A372056. - _Toshitaka Suzuki_, Mar 30 2024

%t sp3[n_]:=Module[{idn=IntegerDigits[n],k=1},While[!PrimeQ[FromDigits[ Join[ idn, PadRight[ {},k,3]]]],k++];FromDigits[Join[idn,PadRight[{},k,3]]]]; sp3/@Drop[Range[40],{3,-1,3}] (* _Harvey P. Dale_, Jul 11 2017 *)

%Y See A372056 for another version.

%Y Cf. A001651, A030431, A112386.

%K nonn,base

%O 1,1

%A _Parthasarathy Nambi_, Dec 05 2005

%E More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Dec 09 2005

%E Edited by _N. J. A. Sloane_, Apr 24 2024. (Escape clause added to definition at the suggestion of _Toshitaka Suzuki_, Mar 30 2024. See also A372056.)