A112394 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.

13, 23, 43, 53, 73, 83, 103, 113, 1333333333333333, 1433, 163, 173, 193, 20333, 223, 233, 2533333333, 263, 283, 293, 313, 323333, 3433, 353, 373, 383

Offset: 1

Author

Parthasarathy Nambi, Dec 05 2005

Keywords

• nonn
• base

Comments

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

Examples

			For k = 1, we get the prime 13.
For k = 13, we get the prime 1333333333333333 (the smaller numbers 133,1333,13333 etc. are not primes).
For k = 4070 and 9287, no such prime exists, so we get -1 for the value. Compare A372056. - _Toshitaka Suzuki_, Mar 30 2024
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..273 (terms 1..200 from Harvey P. Dale)

Crossrefs

See A372056 for another version.

Cf. A001651, A030431, A112386.

Programs

Mathematica

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 *)

Extensions

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

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.)