A241474 - OEIS

%I #9 Apr 23 2014 10:57:52

%S 3,6,5,8,7,9,407,68,11,14,13,18,413,20,17,24,19,22,49,21020,23,25,27,

%T 104,65,32,29,628,31,34,35,40,53,38,37,6136,77,44,41,2140,43,46,4043,

%U 50,47,49,51,56,40049,130,53,652,57,58,95,116,59,62,61,480,65,68

%N Smallest k such that tau(k)=reversal(k-n).

%C tau(n) = A000005(n) is the number of divisors of n.

%C Observation :

%C The sequence shows pairs of the form (m, m +/- 1) such as: (6,5), (8,7), (14,13), (34,35), (38,37), (57,58), (62,61), (74,73), (93,94), (94,95), (104,105), (118,119), (135,136), (142,143), (177,178), (188,187), (244,245), ...

%e a(20)=21020 because tau(21020) = 12 = reversal(21) = reversal(21020-20).

%t Table[k=n+1; While[!(k>n)||!DivisorSigma[0,k]==FromDigits[Reverse[IntegerDigits[k-n]]], k++]; k, {n, 80}]

%o (PARI) rev(n) = subst(Polrev(digits(n)), x, 10);

%o a(n) = {k = n+1; while (numdiv(k) != rev(k-n), k++); k;} \\ _Michel Marcus_, Apr 23 2014

%Y Cf. A000005, A004086.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Apr 23 2014