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A072041 a(n) is the smallest number of the form k + reverse(k) for exactly n integers k, or -1 if no such number exists. 11

%I

%S 1,0,22,33,44,55,66,77,88,99,1111,-1,2552,-1,2662,3443,2772,-1,2882,

%T -1,2992,3663,-1,-1,3773,5445,-1,3883,4664,-1,3993,-1,4774,-1,-1,5665,

%U 4884,-1,-1,-1,4994,-1,6666,-1,-1,5885,-1,-1,6776,7667,5995,-1,-1,-1,6886

%N a(n) is the smallest number of the form k + reverse(k) for exactly n integers k, or -1 if no such number exists.

%C The negative terms are conjectural. Moreover they have a rather low degree of confirmation, since due to the time-consuming computations only numbers from 0 to 65000 have been taken into account. Random tests of larger numbers however seem to indicate, that only selected values of n occur. - In the cognate sequence A071266 two numbers a and b are counted only once, if n = a + b, a = reverse(b), b = reverse(a). Then 33 = 12 + 21 = 30 + 03 has a count of 2 and 44 = 13 + 31 = 22 + 22 = 40 + 04 has a count of 3, so 44 appears in A071266 instead of 33.

%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>

%e a(0) = 1, since 1 can in no way be written as k + reverse(k); a(1) = 0, since 0 = k + reverse(k) for k = 0; a(3) = 33, since 33 = k + reverse(k) for k = 12, 21 and 30.

%Y Cf. A067030, A071266, A072040.

%K base,sign

%O 0,3

%A _Klaus Brockhaus_, Jun 08 2002

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Last modified November 12 14:43 EST 2019. Contains 329058 sequences. (Running on oeis4.)