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A165956
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a(0) = 1. For n >= 1, a(n) = the number of earlier terms that, when written in binary, are substrings in binary n.
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1
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1, 1, 2, 2, 4, 4, 4, 2, 8, 8, 5, 6, 9, 7, 7, 4, 11, 11, 10, 10, 12, 8, 9, 10, 14, 13, 11, 11, 14, 12, 10, 4, 13, 13, 13, 13, 12, 13, 13, 14, 18, 17, 10, 15, 19, 18, 16, 13, 18, 18, 20, 17, 26, 21, 19, 21, 22, 21, 26, 24, 20, 21, 12, 5, 14, 14, 14, 14, 15, 17, 17, 19, 19, 16, 23, 22, 21
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OFFSET
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0,3
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COMMENTS
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If we instead had an offset of 1 and a(1)=1, then we would have sequence A122954.
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LINKS
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EXAMPLE
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13 in binary is 1101. The earlier terms that, when written in binary, are substrings in 1101 are: a(0)=1, a(1)=1, a(2) = 2 = 10 in binary, a(3) = 2 = 10 in binary, a(7) = 2 = 10 in binary, a(10) = 5 = 101 in binary, and a(11) = 6 = 110 in binary. There are 7 such terms, so a(13) = 7.
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PROG
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(Python)
from collections import Counter
A, C = [1], Counter()
for n in range(1, nmax+1):
b = bin(n)[2:]
C.update({bin(A[-1])[2:]})
A.append(sum(C[i] for i in C if b.find(i) != -1))
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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