cp's OEIS Frontend

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.

%I A072041 #9 Aug 28 2024 09:38:11
%S A072041 1,0,22,33,44,55,66,77,88,99,1111,-1,2552,-1,2662,3443,2772,-1,2882,
%T A072041 -1,2992,3663,-1,-1,3773,5445,-1,3883,4664,-1,3993,-1,4774,-1,-1,5665,
%U A072041 4884,-1,-1,-1,4994,-1,6666,-1,-1,5885,-1,-1,6776,7667,5995,-1,-1,-1,6886
%N 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.
%C A072041 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.
%C A072041 Terms are correct for k <= 10^8. - _Sean A. Irvine_, Aug 27 2024
%H A072041 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e A072041 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 A072041 Cf. A067030, A071266, A072040.
%K A072041 base,sign
%O A072041 0,3
%A A072041 _Klaus Brockhaus_, Jun 08 2002