A048411 Squares whose consecutive digits differ by 1.
0, 1, 4, 9, 121, 676, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321
Offset: 1
Programs
-
Haskell
a048411 n = a048411_list !! (n-1) a048411_list = filter ((== 1) . a010052) a033075_list -- Reinhard Zumkeller, Feb 21 2012
-
Mathematica
Select[Range[0, 10^7]^2, Or[# == 0, IntegerLength@ # == 1, Union@ Abs@ Differences@ IntegerDigits@ # == {1}] &] (* Michael De Vlieger, Nov 25 2016 *) -
Python
from sympy.ntheory.primetest import is_square def gen(d, s=None): if d == 0: yield tuple(); return if s == None: yield from [(i, ) + g for i in range(1, 10) for g in gen(d-1, s=i)] else: if s > 0: yield from [(s-1, ) + g for g in gen(d-1, s=s-1)] if s < 9: yield from [(s+1, ) + g for g in gen(d-1, s=s+1)] def afind(maxdigits): print(0, end=", ") for d in range(1, maxdigits+1): for g in gen(d, s=None): t = int("".join(map(str, g))) if is_square(t): print(t, end=", ") afind(17) # Michael S. Branicky, Sep 26 2021
Formula
a(n) = A048412(n)^2.
Comments