login
A176630
Nonpalindromic numbers whose binary representation when reversed is the same as binary representation of the number reversed in decimal.
0
92, 732, 759, 957, 5485, 5845, 71869, 77360, 96817, 319773, 377913, 13162800, 39781062, 79497594, 94729789, 98792749, 144579540, 1231493321, 1233941321, 7075293947, 7493925707, 32817543720, 71461803829, 92830816417
OFFSET
1,1
COMMENTS
The binary representation of a decimal number, when reversed, is also the reverse of the decimal number.
FORMULA
Intersection of A029742 and A081434. - Andrew Howroyd, Jan 14 2020
EXAMPLE
92 = 1011100 mirrors 0011101 = 29.
732 = 1011011100 mirrors 0011101101 = 237.
MATHEMATICA
Select[Range[10^6], And[! PalindromeQ@ #, Drop[#, LengthWhile[#, # == 0 &]] &@ Reverse@ IntegerDigits[#, 2] === IntegerDigits[IntegerReverse[#], 2]] &] (* Michael De Vlieger, Dec 29 2020 *)
PROG
(PARI) is(n)={my(t=fromdigits(Vecrev(digits(n, 10)), 10)); t<>n && t == fromdigits(Vecrev(digits(n, 2)), 2)}
{ for(k=1, 10^6, if(is(k), print1(k, ", "))) } \\ Andrew Howroyd, Jan 14 2020
(Python)
def agen():
k = 0
while True:
strk = str(k)
revstrk = strk[::-1]
if revstrk != strk:
if int(revstrk) == int((bin(k)[2:])[::-1], 2):
yield k
k += 1
g = agen()
print([next(g) for i in range(11)]) # Michael S. Branicky, Dec 29 2020
CROSSREFS
Sequence in context: A107343 A355622 A231300 * A281077 A207061 A279913
KEYWORD
base,more,nonn
AUTHOR
Gil Broussard, Apr 22 2010
EXTENSIONS
Name clarified and a(12)-a(17) from Andrew Howroyd, Jan 14 2020
a(18)-a(24) from Michael S. Branicky, Dec 29 2020
STATUS
approved