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A118655 Numbers k such that Hamming weight of k equals Hamming weight of k^3. 4

%I #18 Jul 16 2023 02:11:41

%S 1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,56953,

%T 65536,113906,131072,227812,262144,455624,524288,911248,1048576,

%U 1822496,1830651,2097152,3644992,3661302,4194304,5502457,7289984,7322604

%N Numbers k such that Hamming weight of k equals Hamming weight of k^3.

%C A000079(n) is a subsequence because the Hamming weight of any A000079(n) is 1 and cubing such a number just adds binary zeros. A077436 is the sequence when the a(n) is squared, not cubed as here.

%H Donovan Johnson, <a href="/A118655/b118655.txt">Table of n, a(n) for n = 1..177</a> (terms <= 2^40)

%F A000120(a(n)) = A000120(a(n)^3).

%t Select[Range[10^6], DigitCount[#, 2, 1] == DigitCount[#^3, 2, 1] &] (* _Amiram Eldar_, Jul 16 2023 *)

%o (PARI) bitcnt(n)= { local(bitv,bitl) ; bitv=binary(n) ; bitvl=matsize(bitv) ; return(sum(i=1,bitvl[2],bitv[i])) ; }

%o { for(i=1,8000000, if(bitcnt(i)==bitcnt(i^3), print1(i,",") ; ) ; ) ; }

%Y Cf. A077436, A000079, A000120.

%K easy,base,nonn

%O 1,2

%A _R. J. Mathar_, May 18 2006

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)