A352535 Numbers m such that A257588(m) = 0.

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 220, 330, 354, 440, 453, 550, 660, 770, 880, 990, 1001, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1221, 1331, 1441, 1487, 1551, 1575, 1661, 1771, 1784, 1881, 1991, 2002, 2112, 2200, 2211, 2222, 2233, 2244, 2255, 2266, 2277

Offset: 1

Author

Bernard Schott, Mar 20 2022

Keywords

• nonn
• base

Comments

If m is a term, 10*m is also a term; so, terms with no trailing zeros are all primitive terms.

Palindromes with even number of digits (A056524) are all terms.

Examples

			354 is a term since 3^2 - 5^2 + 4^2 = 0 (with Pythagorean triple (3,4,5)).
1487 is a term since 1^2 - 4^2 + 8^2 - 7^2 = 0.
		

Crossrefs

Cf. A003132, A257588.

Subsequences: A056524, A333440, A338754.

Programs

Mathematica

f[n_] := Abs @ Total[(d = IntegerDigits[n]^2) * (-1)^Range[Length[d]]]; Select[Range[0, 2300], f[#] == 0 &] (* Amiram Eldar, Mar 20 2022 *)

Python

from itertools import count, islice
def A352535_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda m: not sum(int(d)**2*(-1 if i % 2 else 1) for i, d in enumerate(str(m))), count(max(startvalue,0)))
A352535_list = list(islice(A352535_gen(),30)) # Chai Wah Wu, Mar 24 2022

Formula

A257588(a(n)) = 0.