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 A322000 Nonnegative integers, sorted by increasing value of A028897(n) = Sum d[i]*2^i for n = Sum d[i]*10^i, then value of n. 4
 0, 1, 2, 10, 3, 11, 4, 12, 20, 100, 5, 13, 21, 101, 6, 14, 22, 30, 102, 110, 7, 15, 23, 31, 103, 111, 8, 16, 24, 32, 40, 104, 112, 120, 200, 1000, 9, 17, 25, 33, 41, 105, 113, 121, 201, 1001, 18, 26, 34, 42, 50, 106, 114, 122, 130, 202, 210, 1002, 1010, 19, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A028897(n) is the result of using the decimal digits of n, but weighting their position as in base 2. For sake of brevity we refer to this as the b-value of n in the sequel. This idea is found on the website given in links under the name "decibinary numbers". The b-values increment by 1 at indices (of "records") 1, 2, 4, 6, 10, 14, 20, 26, 36, ... Prefixing an initial 0, the gaps between these, equal to the number of occurrences of a given b-value (0, 1, 2, ...), are 1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 13, 13, ... = A072170(n,10). In this sequence each of (1, 2, 4, 6, 10, 13, 18, ...) is repeated twice. LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Robin C. Yu, Decibinary Numbers, on Hackerrank.com. EXAMPLE The first terms of the sequence are as follows: (b = A028897)   n | 0 | 1 | 2 | 10 | 3 | 11 | 4 | 12 | 20 | 100 | 5 | 13 | 21 | 101 | ... ----+---+---+---+----+---+----+---+----+----+-----+---+----+----+-----+----- b(n)| 0 | 1 | 2 |  2 | 3 |  3 | 4 |  4 |  4 |  4  | 5 |  5 |  5 |  5  | ... For example, b(345) = 3*2^2 + 4*2 + 5 = 25. MAPLE N:= 30: # for all numbers with A028897(n) <= N L:= {seq([i, i], i=0..9)}: Agenda:= {seq([i, i], i=1..9)}: extend:= proc(p) local x;  op(select(t -> t[2]<=N, [seq([10*p[1]+x, 2*p[2]+x], x=0..9)])); end proc: sorter:= proc(p1, p2) if p1[2] <> p2[2] then p1[2] < p2[2] else p1[1] < p2[1] fi end proc: while Agenda <> {} do   Agenda:= map(extend, Agenda);   L:= L union Agenda; od: L:= sort( convert(L, list), sorter): map(t -> t[1], L); # Robert Israel, Feb 24 2019 PROG (PARI) my(A028897(n)=fromdigits(digits(n), 2), S=[]); for(k=1, 2^10, (t=A028897(k))>9||S=setunion(S, [[t, k]])); apply(t->t[2], S) CROSSREFS Cf. A028897, A072170 (see comments). Sequence in context: A342047 A239083 A239084 * A061196 A239136 A239137 Adjacent sequences:  A321997 A321998 A321999 * A322001 A322002 A322003 KEYWORD nonn,base,look AUTHOR M. F. Hasler, Feb 13 2019 STATUS approved

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Last modified June 13 11:33 EDT 2021. Contains 344990 sequences. (Running on oeis4.)