A367547 Euclid's triangle A217831 represented as binary numbers.

0, 11, 10, 110, 1010, 11110, 100010, 1111110, 10101010, 110110110, 1010001010, 11111111110, 100010100010, 1111111111110, 10101000101010, 110100110010110, 1010101010101010, 11111111111111110, 100010100010100010, 1111111111111111110, 10100010101010001010, 110110010110100110110

Offset

0,2

Comments

The sequence represents the rows of Euclid's triangle A217831 as unsigned binary integers. If a '0' is prepended to the most significant bit (for n > 1) the terms can also be seen as palindromic binary strings. The decimal representation of the sequence is A367544.

Links

Table of n, a(n) for n=0..21.

Mathematica

A367547[n_]:=FromDigits[Boole[CoprimeQ[n, Range[0, n]]]];
Array[A367547, 30, 0] (* Paolo Xausa, Nov 24 2023 *)

Prog

(SageMath)  # For Python include 'import math' for math.gcd.
def A367547(n):
    cop = [int(gcd(i, n) == 1) for i in range(n + 1)]
    return int(''.join(map(str, cop)))
print([A367547(n) for n in range(22)])
(PARI) a(n) = fromdigits(vector(n+1, i, gcd(i-1, n)==1), 10); \\ Michel Marcus, Nov 24 2023
(Python)
from math import gcd
def A367547(n): return sum(10**k for k in range(n+1) if gcd(n, k)==1) # Chai Wah Wu, Nov 24 2023

Crossrefs

Cf. A217831, A367544.

Sequence in context: A105028 A331560 A014550 * A070836 A063432 A364121

Adjacent sequences: A367544 A367545 A367546 * A367548 A367549 A367550

Keyword

nonn,base

Author

Peter Luschny, Nov 22 2023

Status

approved