A241474 Smallest k such that tau(k)=reversal(k-n).

3, 6, 5, 8, 7, 9, 407, 68, 11, 14, 13, 18, 413, 20, 17, 24, 19, 22, 49, 21020, 23, 25, 27, 104, 65, 32, 29, 628, 31, 34, 35, 40, 53, 38, 37, 6136, 77, 44, 41, 2140, 43, 46, 4043, 50, 47, 49, 51, 56, 40049, 130, 53, 652, 57, 58, 95, 116, 59, 62, 61, 480, 65, 68

Offset

1,1

Comments

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

Observation :

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), ...

Links

Table of n, a(n) for n=1..62.

Example

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

Mathematica

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

Prog

(PARI) rev(n) = subst(Polrev(digits(n)), x, 10);
a(n) = {k = n+1; while (numdiv(k) != rev(k-n), k++); k; } \\ Michel Marcus, Apr 23 2014

Crossrefs

Cf. A000005, A004086.

Sequence in context: A201418 A123688 A082284 * A259556 A063520 A078677

Adjacent sequences: A241471 A241472 A241473 * A241475 A241476 A241477

Keyword

nonn,base

Author

Michel Lagneau, Apr 23 2014

Status

approved