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4, 5, 6, 7, 4, 5, 6, 7, 12, 13, 14, 15, 12, 13, 14, 15, 20, 21, 22, 23, 20, 21, 22, 23, 28, 29, 30, 31, 28, 29, 30, 31, 36, 37, 38, 39, 36, 37, 38, 39, 44, 45, 46, 47, 44, 45, 46, 47, 52, 53, 54, 55, 52, 53, 54, 55, 60, 61, 62, 63, 60, 61, 62, 63
(list;
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refs;
listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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a(n) = n if n is congruent to (4, 5, 6, 7) mod 8. In general, (n OR 2^k) has the closed form n + 2^k * floor( ( (n+2^k) mod 2^(k+1) )/2^k ).
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LINKS
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FORMULA
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a(n) = (n+4) - (n AND 4).
a(n) = (n XOR 4) + (n AND 4).
a(n) = n + 4*floor(((n+4) mod 8)/4).
a(n) = 2 + n + 2*(-1)^floor(n/4).
G.f.: (4 - 3*x + x^5)/((1 - x)^2*(1 + x^4)). (End)
Sum_{n>=0} (-1)^n/a(n) = (2*sqrt(2)-1)*Pi/8 - 3*log(2)/4. - Amiram Eldar, Aug 07 2023
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EXAMPLE
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a(10) = 14 because 10 in binary is 1010 and 4 is 0100, and 1010 OR 0100 = 1110, which is 14 in decimal.
a(11) = 15 because 11 in binary is 1011 and 4 is 0100, and 1011 OR 0100 = 1111, which is 15 in decimal.
a(12) = 12 because 12 in binary is 1100 and 4 is 0100, and 1100 OR 0100 = 1100, which is 12 in decimal.
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MAPLE
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with(Bits): seq(Or(n, 4), n = 0..60);
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MATHEMATICA
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PROG
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(Magma) [BitwiseOr(n, 4): n in [0..70]]; // Bruno Berselli, Jul 01 2014
(Python)
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CROSSREFS
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Cf. similar sequences listed in A244587.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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