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

1,1

Comments

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

Links

Table of n, a(n) for n=1..23.

Formula

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

Example

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.

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]);

Crossrefs

Cf. A001222, A043096, A043562, A379229.

Sequence in context: A074109 A291101 A036336 * A070842 A086927 A342108

Adjacent sequences: A379532 A379533 A379534 * A379536 A379537 A379538

Keyword

nonn,base

Author

Robert Israel, Jan 07 2025

Status

approved