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 A144477 a(n) = minimal number of 0's that must be changed to 1's in the binary expansion of the n-th prime in order to make it into a palindrome. 1

%I

%S 1,0,0,0,1,1,0,1,1,1,0,1,1,2,1,2,1,1,1,2,0,2,2,1,1,2,1,0,2,2,0,1,1,2,

%T 2,3,1,2,1,1,3,1,1,1,2,1,1,1,1,1,3,1,3,1,0,2,2,3,1,1,2,2,2,3,0,1,3,1,

%U 3,1,2,2,1,1,2,1,2,3,1,2,1,3,1,2,2,0,2,3,2,1,1,1,1,1,2,1,1,1,2,3

%N a(n) = minimal number of 0's that must be changed to 1's in the binary expansion of the n-th prime in order to make it into a palindrome.

%F a(n) is half the Hamming distance between the binary expansion of prime(n) and its reversal.

%e a(5) = 1 since prime(5) = 11 = 1011_2 becomes a palindrome if we change the third bit to 0.

%o (PARI)

%o HD(p)=

%o {

%o v=binary(p); H=0; j=#v;

%o for(k=1,#v, H+=abs(v[k]-v[j]); j--);

%o return(H)

%o };

%o for(n=1,100, p=prime(n); an=HD(p)/2; print1(an,", "))

%Y Subsequence of A037888.

%K nonn,base

%O 1,14

%A _Washington Bomfim_, Jan 15 2011, following a suggestion from _Joerg Arndt_.

%E Edited by _N. J. A. Sloane_, Apr 23 2020 at the suggestion of _Harvey P. Dale_

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Last modified September 20 08:53 EDT 2021. Contains 347579 sequences. (Running on oeis4.)