A379535 a(n) is the least number that has n prime factors, counted by multiplicity, and n runs in its decimal representation.

2, 10, 102, 1012, 10104, 101010, 1010124, 10101216, 101010176, 1010101504, 10101010304, 101010101248, 1010101013280, 10101010101248, 101010101013504, 1010101010137856, 10101010101010432, 101010101010145280, 1010101010101010432, 10101010101010497536, 101010101010101084160, 1010101010101010620416, 10101010101010105368576

Offset: 1

Author

Robert Israel, Jan 07 2025

Keywords

• nonn
• base

Comments

Is a(n) always an n-digit member of A043096, i.e. a number with all pairs of adjacent digits distinct?

Examples

			a(4) = 1012 because 1012 = 2^2 * 11 * 23 has 4 prime factors, counted with multiplicity, and 4 runs in its decimal representation, and no smaller number works.
		

Crossrefs

Cf. A001222, A043096, A043562, A379229.

Programs

Maple

f:= proc(n)
  local x,x0,L,t,i;
  if n::odd then x0:= (10^(n+1)-1)/99 else x0:= (10^(n+1)-10)/99 fi;
  for x from x0 do
    L:= convert(x,base,10);
    t:= nops(L) - numboccur(0, L[2..-1]-L[1..-2]);
    if t = n and numtheory:-bigomega(x) = n then return x fi
  od
end proc:
map(f, [$1..23]);

Formula

A001222(a(n)) = A043562(a(n)) = n.