A238171 Numbers n such that n+(n+1) = n'+(n+1)', where n' is the arithmetic derivative of n.

16, 108, 3294172, 7975979

Offset

1,1

Comments

a(5) > 10^13. - Giovanni Resta, Mar 13 2014

a(5) > 5*10^13. - Hiroaki Yamanouchi, Aug 27 2015

Links

Table of n, a(n) for n=1..4.

Example

16' = 32, 17' = 1 and 16 + 17 = 32 + 1 = 33.
108' = 216, 109' = 1 and 108 + 109 = 216 + 1 = 217.
3294172' = 6588344, 3274173' = 1 and 3294172 + 3294173 = 6588344 + 1 = 6588345.
7975979' = 941063, 7975980' = 15010896 and 7975979 + 7975980 = 941063 + 15010896 = 15951959.

Maple

with(numtheory); P:= proc(q) local a, b, n, p; for n from 1 to q do
a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
b:=(n+1)*add(op(2, p)/op(1, p), p=ifactors(n+1)[2]);
if 2*n+1=a+b then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A003415.

Sequence in context: A165558 A337391 A250425 * A155871 A120668 A053526

Adjacent sequences: A238168 A238169 A238170 * A238172 A238173 A238174

Keyword

nonn,more

Author

Paolo P. Lava, Feb 19 2014

Status

approved