A035928 -id:A035928 - cp's OEIS frontend

A279624 Numbers x such that BCR(x) = R(x), where BCR = binary-complement-and-reverse = take one's complement then reverse bit order and R(x) is the digits reverse of n.

2, 61, 212, 232, 666, 868, 2222, 642246, 687588, 820491, 885786, 2283822, 2459542, 2807082, 2860682, 45377354, 214878412, 841191148, 841740971, 49126162194

Offset: 1

Paolo P. Lava, Dec 16 2016

			687588 in base 2 is 10100111110111100100. Its binary-complement-and-reverse is 11011000010000011010, which is 885786 in base 10.

Cf. A004086, A035928, A036044.

with(numtheory): T:=proc(w) local x, y, z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
P:=proc(q) local a,b, k,n; for n from 1 to q do a:=convert(n,base,2); b:=0;
for k from 1 to nops(a) do if a[k]=0 then a[k]:=1 else a[k]:=0; fi; b:=2*b+a[k]; od;
if b=n then print(n); fi; od; end: P(10^6);

Select[Range[10^6], MatchQ @@ {FromDigits[#, 2] &@ Reverse[ IntegerDigits[#, 2] /. {0 -> 1, 1 -> 0}], FromDigits@ Reverse@ IntegerDigits@ #} &] (* Michael De Vlieger, Dec 16 2016 *)

a(17)-a(20) from Hans Havermann, Dec 23 2016

A303610 Circle aliasing numbers with 1/n size steps.

Original entry on oeis.org

10, 1010, 110100, 11010100, 1101100100, 110110100100, 11101010101000, 1110110101001000, 111011010101001000, 11101101101001001000, 1110111010101010001000, 111011101010101010001000, 11110110110101010010010000, 1111011011010101010010010000, 111101110101101010010100010000

Offset: 1

Ben Paul Thurston, May 06 2018

nonn

Starting from [-1,0] taking 2*n steps of length 1/n each either up or right, follow the path staying as close to the unit circle as possible. Every step up is considered a 1, every step right is considered a 0.

			For n=3, we have 110100, meaning if we were to start at [-1, 0] and take 2*n=6 steps of length 1/n = 1/6 which can either be up or to the right, to follow the path of the unit circle the closest we would move up 1, up 1 again, then right, then up again, then right two more times, which we translate to the binary number 110100.

Subsequence of A035928 in binary.

def closer(pos1, pos2):
    dpos1 = (pos1[0]**2.0+pos1[1]**2.0)**.5
    dpos2 = (pos2[0]**2.0+pos2[1]**2.0)**.5
    if (1.0-dpos1)**2.0 < (1.0-dpos2)**2.0:
        return True
    else:
        return False
def converts(path):
    return ''.join(path)
l = []
for steps in range(1, 20):
    stepsize = 1.0/steps
    pos = [-1.0, 0.0]
    paths = []
    for i in range(0, 2*steps):
        if closer([pos[0]+stepsize, pos[1]], [pos[0], pos[1]+stepsize]):
            pos = [pos[0]+stepsize, pos[1]]
            paths.append(str(0))
        else:
            pos = [pos[0], pos[1]+stepsize]
            paths.append(str(1))
    l.append(int(converts(paths)))
print(l)

A351174 Smallest antipalindromic natural number k such that k*A351172(n) is also antipalindromic.

Original entry on oeis.org

2, 2, 2, 10, 10, 52, 2, 12, 2, 10, 2, 2, 42, 883732, 178, 52, 38, 986352, 56, 3784, 42, 52, 2, 56, 738, 2, 12, 666, 2490513625334, 178, 2, 2254, 2, 10, 595318, 42, 2, 2, 2, 2, 48976179602, 170, 10426, 10, 722, 150, 170, 36622, 55501364, 10, 52, 204, 10, 170

Offset: 1

Jeffrey Shallit, Feb 04 2022

Here "antipalindromic" means an element of A035928.

			For n = 6 we have a(n) = 52 and A351172(6) = 18, and 52*18 = 936 is antipalindromic.

Cf. A351172, A035928.

cp's OEIS Frontend

A279624 Numbers x such that BCR(x) = R(x), where BCR = binary-complement-and-reverse = take one's complement then reverse bit order and R(x) is the digits reverse of n.

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A303610 Circle aliasing numbers with 1/n size steps.

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Python

A351174 Smallest antipalindromic natural number k such that k*A351172(n) is also antipalindromic.

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