A370046 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number whose binary value is a substring of the binary value of the sum of all previous terms.
1, 2, 3, 6, 4, 8, 12, 9, 5, 18, 17, 10, 7, 19, 14, 16, 11, 20, 13, 24, 22, 15, 32, 36, 34, 25, 23, 37, 27, 21, 26, 64, 69, 40, 43, 29, 30, 35, 39, 44, 28, 42, 53, 129, 72, 38, 31, 81, 45, 50, 46, 47, 49, 74, 41, 54, 55, 51, 52, 57, 58, 128, 68, 70, 140, 77, 60, 139, 85, 33, 75, 61, 59, 62, 48
Offset: 1
Examples
a(7) = 12 as the sum of all previous terms is 1 + 2 + 3 + 6 + 4 + 8 = 24 = 11000_2 and 12 = 1100_2 is the smallest unused number that is a substring of "11000".
Links
- Scott R. Shannon, Table of n, a(n) for n = 1..10000
- Scott R. Shannon, Image of the first 50000 terms.
Programs
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Python
from itertools import islice def agen(): # generator of terms s, mink, aset = 3, 3, {1, 2} yield from [1, 2] while True: an, ss = mink, bin(s)[2:] while an in aset or not bin(an)[2:] in ss: an += 1 aset.add(an); s += an; yield an while mink in aset: mink += 1 print(list(islice(agen(), 75))) # Michael S. Branicky, Feb 08 2024
Formula
a(n) = A317788(n) for any n >= 3. - Rémy Sigrist, Feb 09 2024
Comments