A086067 -id:A086067 - cp's OEIS frontend

A086066 a(n) = Sum_{d in D(n)} 2^d, where D(n) = set of digits of n in decimal representation.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 3, 2, 6, 10, 18, 34, 66, 130, 258, 514, 5, 6, 4, 12, 20, 36, 68, 132, 260, 516, 9, 10, 12, 8, 24, 40, 72, 136, 264, 520, 17, 18, 20, 24, 16, 48, 80, 144, 272, 528, 33, 34, 36, 40, 48, 32, 96, 160, 288, 544, 65, 66, 68, 72, 80

Offset: 0

Reinhard Zumkeller, Jul 08 2003

For bitwise logical operations AND and OR:
a(m) = (a(m) AND a(n)) iff D(m) is a subset of D(n),
(a(m) AND a(n)) = 0 iff D(m) and D(n) are disjoint,
a(m) = (a(m) OR a(n)) iff D(n) is a subset of D(m),
a(m) = a(n) iff D(m) = D(n);
A086067(n) = A007088(a(n)).
From Reinhard Zumkeller, Sep 18 2009: (Start)
a(A052382(n)) mod 2 = 0; a(A011540(n)) mod 2 = 1;
for n > 0: a(A000004(n))=1, a(A000042(n))=2, a(A011557(n))=3, a(A002276(n))=4, a(A111066(n))=6, a(A002277(n))=8, a(A002278(n))=16, a(A002279(n))=32, a(A002280(n))=64, a(A002281(n))=128, a(A002282(n))=256, a(A002283(n))=512;
a(n) <= 1023. (End)

			n=242, D(242) = {2,4}: a(242) = 2^2 + 2^4 = 20.

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

A086066 := proc(n) local d: if(n=0)then return 1: fi: d:=convert(convert(n,base,10),set): return add(2^d[j],j=1..nops(d)): end: seq(A086066(n),n=0..64); # Nathaniel Johnston, May 31 2011

A086068 Min{k: A086066(k) = n}.

Original entry on oeis.org

0, 1, 10, 2, 20, 12, 102, 3, 30, 13, 103, 23, 203, 123, 1023, 4, 40, 14, 104, 24, 204, 124, 1024, 34, 304, 134, 1034, 234, 2034, 1234, 10234, 5, 50, 15, 105, 25, 205, 125, 1025, 35, 305, 135, 1035, 235, 2035, 1235, 10235, 45, 405, 145, 1045, 245, 2045

Offset: 1

Reinhard Zumkeller, Jul 08 2003

Sequence is finite with last term a(2^10-1)=a(1023)=1023456789; A086067(1023456789)=1111111111.

Nathaniel Johnston, Table of n, a(n) for n = 1..1023 (full sequence)

Cf. A086069, A086070, A086067.

A086068 := proc(n) local b,k,s: s:={}: if(n=1)then return 0: fi: b:=convert(n,base,2): for k from 1 to nops(b) do if(b[k] = 1)then s:=s union {k-1}: fi: od: s:=sort(convert(s,list)): if(s[1]=0)then return s[2]*10^(nops(s)-1)+add(s[j]*10^(nops(s)-j),j=3..nops(s)): else return add(s[j]*10^(nops(s)-j),j=1..nops(s)): fi: end: seq(A086068(n),n=1..53); # Nathaniel Johnston, Jun 01 2011

A086084 A086070 in binary.

Original entry on oeis.org

1, 10, 11, 101, 111, 1011, 1101, 1111, 10111, 11011, 11101, 11111, 101111, 110111, 111011, 111101, 111111, 1011111, 1101111, 1110111, 1111011, 1111101, 1111111, 10111111, 11011111, 11101111, 11110111, 11111011, 11111101

Offset: 1

Reinhard Zumkeller, Jul 08 2003

a(n) = A007088(A086070(n)).

Nathaniel Johnston, Table of n, a(n) for n = 1..47 (full sequence)

Cf. A086067, A086068, A086069.

cp's OEIS Frontend

A086066 a(n) = Sum_{d in D(n)} 2^d, where D(n) = set of digits of n in decimal representation.

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A086068 Min{k: A086066(k) = n}.

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A086084 A086070 in binary.

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