

A144477


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


1



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, 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, 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
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OFFSET

1,14


LINKS

Table of n, a(n) for n=1..100.


FORMULA

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


EXAMPLE

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


PROG

(PARI)
HD(p)=
{
v=binary(p); H=0; j=#v;
for(k=1, #v, H+=abs(v[k]v[j]); j);
return(H)
};
for(n=1, 100, p=prime(n); an=HD(p)/2; print1(an, ", "))


CROSSREFS

Subsequence of A037888.
Sequence in context: A159847 A327489 A257886 * A106345 A319395 A194636
Adjacent sequences: A144474 A144475 A144476 * A144478 A144479 A144480


KEYWORD

nonn,base


AUTHOR

Washington Bomfim, Jan 15 2011, following a suggestion from Joerg Arndt.


EXTENSIONS

Edited by N. J. A. Sloane, Apr 23 2020 at the suggestion of Harvey P. Dale


STATUS

approved



