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A364165
a(n) is the least prime factor of the concatenation of 2^n and 3^n.
0
11, 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.
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
KEYWORD
nonn,base
AUTHOR
Robert Israel, Jul 12 2023
EXTENSIONS
Duplicated terms (former a(11)-a(20)) removed by Georg Fischer, May 23 2024
STATUS
approved