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.

1, 2, 14, 70, 166, 350, 1050, 2002, 1870, 4730, 5170, 9350, 15106, 29050, 45318, 65450, 25850, 139590, 75530, 129250, 180950, 226590, 383350, 341530, 377650, 551650, 697950, 439450, 1127610, 1489950, 1004850, 1654950

Offset: 1

Author

Reinhard Zumkeller, May 21 2015

Keywords

• nonn

Comments

A099305(a(n)) = n and A099305(m) != n for m < a(n).

Examples

			a(3) = 14, 14' = 19:
1:  (14 + 7)' = 21' = 10, and 14' + 7' = 9 + 1 = 10,
2:  (14 + 11)' = 25' = 10, and 14' + 11' = 9 + 1 = 10,
3:  (14 + 28)' = 42' = 41, and 14' + 28' = 9 + 32 = 41;
a(4) = 70: 70' = 59:
1:  (70 + 8)' = 78' = 71, and 70' + 8' = 59 + 12 = 71,
2:  (70 + 35)' = 105' = 71, and 70' + 35' = 59 + 12 = 71,
3:  (70 + 55)' = 125' = 75, and 70' + 55' = 59 + 16 = 75,
4:  (70 + 140)' = 210' = 247, and 70' + 140' = 59 + 188 = 247.
		

Links

• Manfred Scheucher, C Code

Crossrefs

Cf. A099305, A003415.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a258138 = (+ 1) . fromJust . (`elemIndex` a099305_list)

Extensions

More terms from Manfred Scheucher, May 23 2015, May 25 2015