cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A273993 Numbers whose derivative is equal to the arithmetic derivative.

Original entry on oeis.org

0, 1, 2, 10, 22, 34, 38, 46, 94, 134, 142, 158, 262, 382, 514, 526, 542, 766, 2062, 2078, 2174, 2302, 2558, 4126, 4222, 7871, 8198, 8222, 8254, 8318, 10238, 12286, 16894, 32894, 40958, 65542, 65566, 65662, 66046, 67582, 131074, 131078, 131086, 131102, 131198, 132094
Offset: 1

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Author

Paolo P. Lava, Jun 08 2016

Keywords

Examples

			10 in base 2 is 1010 and its derivative is (1+0)(0+1)(1+0)-> 111 that is 7 in base 10 and 7 is also the arithmetic derivative of 10.
		

Crossrefs

Programs

  • Maple
    with(numtheory): P:=proc(q) local a,b,i,n,p;
    for n from 0 to q do a:=0; b:=convert(n,base,2);
    for i from 1 to nops(b)-1 do a:=a+((b[i]+b[i+1]) mod 2)*2^(i-1); od;
    if a=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]) then print(n); fi;
    od; end: P(10^6);

Formula

Solution of the equation A003415(n) = A038554(n).