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A144477
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The n-th prime in binary becomes a palindrome when at least a(n) bits one are changed to zero.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,14
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COMMENTS
| We can change a(n) bits zero to bits one instead.
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FORMULA
| a(n) is half the Hamming distance from prime(n) to the reverse of prime(n).
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EXAMPLE
| a(5) = 1 since prime(5)=11=(1011)2 becomes a palindrome if we change the bit zero to one.
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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, ", "))
- Washington Bomfim, Jan 15 2011
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CROSSREFS
| Subsequence of A037888.
Sequence in context: A165022 A030338 A159847 * A106345 A194636 A081729
Adjacent sequences: A144474 A144475 A144476 * A144478 A144479 A144480
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KEYWORD
| nonn,base
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AUTHOR
| Washington Bomfim (webonfim(AT)gmail.com), Jan 15 2011. From a suggestion of Joerg Arndt.
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