A273993 Numbers whose derivative is equal to the arithmetic derivative.
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
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.
Links
- Paolo P. Lava, Table of n, a(n) for n = 1..78
Programs
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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);