A144477 - OEIS

%I #23 Nov 13 2023 17:54:07

%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.

%H Paolo Xausa, <a href="/A144477/b144477.txt">Table of n, a(n) for n = 1..10000</a>

%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.

%t A144477[n_]:=With[{p=IntegerDigits[Prime[n],2]},HammingDistance[p,Reverse[p]]/2];Array[A144477,100] (* _Paolo Xausa_, Nov 13 2023 *)

%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_