A333440 -id:A333440 - cp's OEIS frontend

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

Bernard Schott, Mar 20 2022

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.

			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.

Cf. A003132, A257588.

Subsequences: A056524, A333440, A338754.

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

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

A257588(a(n)) = 0.

A333441 Numbers where each binary digit can be paired with a digit of the same value at another position so that two pairs can be nested but cannot otherwise overlap.

Original entry on oeis.org

0, 3, 9, 12, 15, 33, 36, 39, 45, 48, 51, 54, 57, 60, 63, 129, 132, 135, 141, 144, 147, 150, 153, 156, 159, 165, 177, 180, 183, 189, 192, 195, 198, 201, 204, 207, 210, 216, 219, 222, 225, 228, 231, 237, 240, 243, 246, 249, 252, 255, 513, 516, 519, 525, 528, 531

Offset: 1

Rémy Sigrist, Mar 21 2020

The term 0 is included by convention (we consider here that it has no digit).
This sequence is a binary variant of A333440.
Every term belong to A059012.
This sequence has connections with A014486; in both sequences digits are balanced in some way.

			The first terms, alongside their binary representation with a possible pairing, are:
  n   a(n)  bin(a(n))
  --  ----  ------------
   1     0  0
   2     3  (11)
   3     9  (1(00)1)
   4    12  (11)(00)
   5    15  (11)(11)
   6    33  (1(00)(00)1)
   7    36  (1(00)1)(00)
   8    39  (1(00)1)(11)
   9    45  (1(0(11)0)1)
  10    48  (11)(00)(00)
  11    51  (11)(00)(11)
  12    54  (11)(0(11)0)
  13    57  (11)(1(00)1)
  14    60  (11)(11)(00)
  15    63  (11)(11)(11)

Rémy Sigrist, Table of n, a(n) for n = 1..8789 (terms < 2^16)

Cf. A014486, A059012, A333440.

is(n, base=2) = { my (u=0, s=0); while (n, my (d=n%base); if (u && s%base==d, u--; s\=base, u++; s=s*base+d); n\=base); u==0 }

cp's OEIS Frontend

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

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