A239724 Composite numbers n such that if n = a U b (where U denotes concatenation) then a’ + b’ = n’, where a’, b’ and n’ are the arithmetic derivatives of a, b and n.

169, 209, 1027, 1219, 1339, 1929, 1966, 2581, 11569, 17251, 17845, 18419, 26093, 59987, 98699, 106159, 107629, 115069, 131179, 137533, 147019, 150071, 151519, 155471, 168505, 186911, 188297, 207413, 217999, 221027, 230183, 231437, 276413, 298891, 368813, 400921

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

The arithmetic derivative of 2581 is 118. Consider 2581 = 25 U 81. The arithmetic derivative of 25 is 10 and of 81 is 108. Therefore we have 10 + 108 = 118.

Maple

with(numtheory); T:=proc(t) local w, x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a, b, c, d, f, g, i, n, p; for n from 1 to q do if not isprime(n) then b:=T(n);
a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]); for i from 1 to b-1 do c:=trunc(n/10^i); d:=n-c*10^i;
f:=c*add(op(2, p)/op(1, p), p=ifactors(c)[2]); g:=d*add(op(2, p)/op(1, p), p=ifactors(d)[2]);
if f+g=a then print(n); break; fi; od; fi; od; end: P(10^9);

Crossrefs

Cf. A003415.

Sequence in context: A044869 A260055 A235718 * A038512 A350705 A141075

Adjacent sequences: A239721 A239722 A239723 * A239725 A239726 A239727

Keyword

nonn,base

Author

Paolo P. Lava, Mar 25 2014

Status

approved