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A265326
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n-th prime minus its binary reversal.
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4
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1, 0, 0, 0, -2, 2, 0, -6, -6, 6, 0, -4, 4, -10, -14, 10, 4, 14, -30, -42, 0, -42, -18, 12, 30, 18, -12, 0, 18, 42, 0, -62, -8, -70, -20, -82, -28, -34, -62, -8, -26, 8, -62, 62, 34, -28, 8, -28, 28, 62, 82, -8, 98, 28, 0, -186, -84, -210, -60
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listen;
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OFFSET
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1,5
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COMMENTS
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The graph consists of a succession of parallelograms. The parallelograms end when there is a long run of mostly positive terms followed by a long run of mostly negative terms. The places where the successive parallelograms end are the primes just before a power of 2: 3, 7, 13, 31, 61, 127, 251, 509, 1021, 2039, 4093, 8191, 16381, 32749, ..., which are terms with indices 2, 4, 6, 11, 18, 31, 54, 97, 172, 309, 564, 1028, 1900, 3512, 6542, 12251, 23000, 43390, 82025, ... (see A014234 and A007053). - N. J. A. Sloane, May 29 2016
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LINKS
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N. J. A. Sloane and Brady Haran, Amazing Graphs, Numberphile video (2019)
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FORMULA
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EXAMPLE
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n=5: prime(5) = 11_10 = 1011_2, reversing gives 1101_2 = 13_10, so a(5) = 11-13 = -2.
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MAPLE
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revdigs:= proc(n) local L, j;
L:= convert(n, base, 2);
add(L[-j]*2^(j-1), j=1..nops(L))
end proc:
map(t -> t - revdigs(t), select(isprime, [2, seq(i, i=3..1000, 2)])); # Robert Israel, Dec 08 2015
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MATHEMATICA
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Table[# - FromDigits[Reverse@ IntegerDigits[#, 2], 2] &@ Prime@ n, {n, 60}] (* Michael De Vlieger, Dec 09 2015 *)
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PROG
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(PARI) a098957(n) = my(v=binary(prime(n)), s); forstep(i=#v, 1, -1, s+=s+v[i]); s
a(n) = prime(n) - a098957(n); \\ Altug Alkan, Dec 07 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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