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, 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

Offset: 1

Author

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

Keywords

• nonn
• base

Examples

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

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A037888.

Programs

Mathematica

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

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,", "))

Formula

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

Extensions

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