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A152754
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"Upper positive integers": n is in the sequence iff in the representation n=A000695(k)+2*A000695(l) satisfies inequality A000695(k) < A000695(l)
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4
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2, 8, 9, 10, 11, 14, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 50, 56, 57, 58, 59, 62, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160
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OFFSET
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1,1
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COMMENTS
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In the mapping: every integer m corresponds to a unique pair (k,l) with m=A000695(k)+2*A000695(l) (k=A059905(m), l=A059906(m)), the numbers a(n) are mapped into the lattice points lying upper the diagonal l=k. If the binary expansion of N is Sum b_j*2^j, then N is in the sequence iff Sum b_(2j)*2^j<Sum b_(2j+1)*2^j. Therefore "in average" satisfies the condition of A139370. This explains, somewhat, why many terms of the sequence are in A139370 as well.
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LINKS
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MATHEMATICA
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fh[n_, h_] := If[h==1, Mod[n, 2], If[Mod[n, 4]>=2, 1, 0]]; half[n_, h_ ] := Module[{t=1, s=0, m=n}, While[m>0, s += fh[m, h]*t; m=Quotient[m, 4]; t *= 2]; s]; mb[n_] := FromDigits[Riffle[IntegerDigits[n, 2], 0], 2]; aQ[n_] := mb[half[n, 1]] < mb[half[n, 2]]; Select[Range[160], aQ] (* Amiram Eldar, Dec 16 2018 from the PARI code *)
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PROG
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(PARI) a000695(n) = fromdigits(binary(n), 4);
half1(n) = { my(t=1, s=0); while(n>0, s += (n%2)*t; n \= 4; t *= 2); (s); }; \\ A059905
half2(n) = { my(t=1, s=0); while(n>0, s += ((n%4)>=2)*t; n \= 4; t *= 2); (s); }; \\ A059906
isok(n) = a000695(half1(n)) < a000695(half2(n)); \\ Michel Marcus, Dec 15 2018
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CROSSREFS
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KEYWORD
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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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