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A048730
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Differences between A008589 (multiples of 7) and A048727, a(n) = ((n*7)-Xmult(n,7)).
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7
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0, 0, 0, 12, 0, 8, 24, 28, 0, 0, 16, 28, 48, 56, 56, 60, 0, 0, 0, 12, 32, 40, 56, 60, 96, 96, 112, 124, 112, 120, 120, 124, 0, 0, 0, 12, 0, 8, 24, 28, 64, 64, 80, 92, 112, 120, 120, 124, 192, 192, 192, 204, 224, 232, 248
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OFFSET
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0,4
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COMMENTS
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For n = binary n[k],n[k-1],...,n[0], bits a(n) = binary b[k+1],b[k],...,b[0] are b[i] = 1 when n[i-1] + n[i-2] + n[i-3] >= 2, so the majority bit 0 or 1 among the 3 bits of n below position i (with 0 bits below the radix point of n as necessary). This is since 7*n = 4*n + 2*n + n is n[i-1] + n[i-2] + n[i-3] at position i-1, and 4*n XOR 2*n XOR n is the same but no carry, so b[i] is the carry only. - Kevin Ryde, Mar 26 2021
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LINKS
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PROG
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(Python)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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