A351904 a(n) is the smallest number k such that the symmetric representation of sigma(k) has at least one subpart n.

1, 3, 2, 7, 9, 11, 4, 15, 10, 19, 6, 14, 24, 27, 8, 31

Offset

1,2

Comments

Conjecture: there are infinitely many pairs of the form a(x) = y; a(y) = x (see examples).

First differs from A351903 at a(11).

Links

Table of n, a(n) for n=1..16.

Example

For n = 11 we have that 6 is the smallest number k with at least one subpart 11 in the symmetric representation of sigma(k), so a(11) = 6.
The symmetric representation of sigma(6) in the first quadrant looks like this:
.
   _ _ _ _
  |_ _ _  |_ 1
        | |_|_ 11
        |_ _  |
            | |
            | |
            |_|
.
There are one subpart 11 and one subpart 1.
.
Some pairs of the form a(x) = y; a(y) = x:
   a(2) =  3;   a(3) =  2.
   a(4) =  7;   a(7) =  4.
   a(6) = 11;  a(11) =  6.
   a(8) = 15;  a(15) =  8.
  a(16) = 31;  a(31) = 16.
.

Crossrefs

Row 1 of A352015.

Cf. A351903 (Analog for parts).

Cf. A000079, A000203, A000225, A001227 (number of subparts), A196020, A235791, A236104, A237270, A237271, A237591, A237593, A279387 (definition of subparts), A280850, A280851 (subparts), A296508, A296513, A347529, A351819.

Sequence in context: A257326 A374611 A118966 * A351903 A359973 A348535

Adjacent sequences: A351901 A351902 A351903 * A351905 A351906 A351907

Keyword

nonn,more

Author

Omar E. Pol, Feb 25 2022

Status

approved