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A144477
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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.
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2
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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
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1,14
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LINKS
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FORMULA
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a(n) is half the Hamming distance between the binary expansion of prime(n) and its reversal.
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EXAMPLE
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a(5) = 1 since prime(5) = 11 = 1011_2 becomes a palindrome if we change the third bit to 0.
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MATHEMATICA
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A144477[n_]:=With[{p=IntegerDigits[Prime[n], 2]}, HammingDistance[p, Reverse[p]]/2]; Array[A144477, 100] (* Paolo Xausa, Nov 13 2023 *)
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PROG
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(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, ", "))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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