A364165 a(n) is the least prime factor of the concatenation of 2^n and 3^n.

11, 23, 7, 827, 41, 19, 7, 1282187, 2566561, 1163, 7, 23, 7, 827, 41, 19, 7, 1282187, 2566561, 1163, 7, 79, 41, 167, 7, 11, 17, 17, 7, 29, 41, 209715210460353203, 7, 838860894143178827, 2566561, 11, 7, 35393, 29, 179, 7, 19, 673, 85899345925559060566555523, 7, 47, 41, 29, 7, 661, 5441, 79, 7, 23

Offset

0,1

Comments

a(n) = 7 if 3^n has d digits where 3^d + 5^n == 0 (mod 7).

a(n) is the concatenation of 2^n and 3^n if n is in A268111.

Links

Table of n, a(n) for n=0..53.

Example

a(5) = 19 because the concatenation of 2^5 and 3^5 is 32243 = 19 * 1697.

Maple

f:= proc(n) local b, v, F;
  b:= 3^n;
  v:= 2^n*10^(1+ilog10(b)) + b;
  F:= select(type, ifactors(v, easy)[2][.., 1], integer);
  if F <> [] then return min(F) fi;
  min(ifactors(v)[2][..., 1]);
end proc;
map(f, [$0..90]);

Crossrefs

Cf. A000079, A000244, A268111.

Sequence in context: A155973 A351849 A253684 * A180481 A110044 A032663

Adjacent sequences: A364162 A364163 A364164 * A364166 A364167 A364168

Keyword

nonn,base

Author

Robert Israel, Jul 12 2023

Status

approved