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A258138 Smallest m, such that there are exactly n solutions of the equation (m+k)' = m' + k', where 1 <= k <= 2*m and x' = A003415(x), the arithmetic derivative of x.

%I A258138 #13 May 25 2015 19:14:49
%S A258138 1,2,14,70,166,350,1050,2002,1870,4730,5170,9350,15106,29050,45318,
%T A258138 65450,25850,139590,75530,129250,180950,226590,383350,341530,377650,
%U A258138 551650,697950,439450,1127610,1489950,1004850,1654950
%N A258138 Smallest m, such that there are exactly n solutions of the equation (m+k)' = m' + k', where 1 <= k <= 2*m and x' = A003415(x), the arithmetic derivative of x.
%C A258138 A099305(a(n)) = n and A099305(m) != n for m < a(n).
%H A258138 Manfred Scheucher, <a href="/A258138/a258138.c.txt">C Code</a>
%e A258138 a(3) = 14, 14' = 19:
%e A258138 1:  (14 + 7)' = 21' = 10, and 14' + 7' = 9 + 1 = 10,
%e A258138 2:  (14 + 11)' = 25' = 10, and 14' + 11' = 9 + 1 = 10,
%e A258138 3:  (14 + 28)' = 42' = 41, and 14' + 28' = 9 + 32 = 41;
%e A258138 a(4) = 70: 70' = 59:
%e A258138 1:  (70 + 8)' = 78' = 71, and 70' + 8' = 59 + 12 = 71,
%e A258138 2:  (70 + 35)' = 105' = 71, and 70' + 35' = 59 + 12 = 71,
%e A258138 3:  (70 + 55)' = 125' = 75, and 70' + 55' = 59 + 16 = 75,
%e A258138 4:  (70 + 140)' = 210' = 247, and 70' + 140' = 59 + 188 = 247.
%o A258138 (Haskell)
%o A258138 import Data.List (elemIndex); import Data.Maybe (fromJust)
%o A258138 a258138 = (+ 1) . fromJust . (`elemIndex` a099305_list)
%Y A258138 Cf. A099305, A003415.
%K A258138 nonn
%O A258138 1,2
%A A258138 _Reinhard Zumkeller_, May 21 2015
%E A258138 More terms from _Manfred Scheucher_, May 23 2015, May 25 2015