“super-d numbers : d*n^d contains ‘d…d’”

  • oeis.org/A032743: super-2 numbers
  • oeis.org/A014569: super-3 numbers
  • oeis.org/A032744: super-4 numbers
  • …
  • oeis.org/A032749: super-9 numbers

Giovanni Resta, super-d numbers, personal web site “Numbers Aplenty”, 2013

PROG

(PARI)

select( {is_A032743(n, d=2, m=10^d, r=m\9*d)=n=d*n^d; until(r>n\=10, n%m==r && return(1))}, [0..999]) \\ _M. F. Hasler_, Jul 16 2024

(Python)

is_A032743=lambda n, d=2: str(d)*d in str(d*n**d) # _M. F. Hasler_, Jul 16 2024