A372262 a(n) = smallest number m > 0 such that n followed by m 3's yields a prime, or -1 if no such m exists.

1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 14, 2, -1, 1, 1, -1, 1, 3, -1, 1, 1, -1, 8, 1, -1, 1, 1, -1, 1, 4, -1, 2, 1, -1, 1, 1, -1, 483, 2, -1, 1, 1, -1, 1, 2, -1, 2, 1, -1, 1, 2, -1, 3, 1, -1, 6, 1, -1, 1, 5, -1, 1, 1, -1, 1, 1, -1, 5, 3, -1, 1, 1, -1, 3, 1, -1, 2, 4

Offset: 1

Author

Toshitaka Suzuki, Apr 24 2024

Keywords

• sign
• base

Comments

a(n) = -1 when n = 3*k because no matter how many 3's are appended to n, the resulting number is always divisible by 3 and therefore cannot be prime.

a(n) = -1 when n = 37037*k + 2808, 3666, 4070, 9287, 18799, 21574, 28083, 30558, 33300, 33740, 36663 or 36707, because n followed by any positive number, m say, of 3's is divisible by at least one of the primes {7,11,13,37}.

a(817) > 300000 or a(817) = -1.

Examples

			a(20)=3 because 203 and 2033 are composite but 20333 is prime.
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..816

Crossrefs

Cf. A372056, A090584, A069568, A363922.

Programs

Mathematica

snm[n_]:=Module[{k=1},If[Mod[n,3]==0,-1,While[CompositeQ[FromDigits[ PadRight[ IntegerDigits[ n],k+ IntegerLength[ n],3]]],k++];k]]; Array[snm,80] (* Harvey P. Dale, Aug 06 2024 *)