A162467 Numbers n such that the sum of all proper substrings of their decimal representation equals the reverse of n.

0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 891, 941, 2931, 51070, 147970, 1330550, 1523870, 75914061, 30735249050, 32036090950, 90000000001, 575605978451, 922898423231, 21326410034240, 31829906273560, 93336794910541, 39470358768890551

Offset

1,2

Comments

Here substrings are substrings of adjacent digits of length less than the number of digits of n, of which there are (d+2)*(d-1)/2=A000096(d-1), counted with multiplicity, where d=A055642(N).

Links

Ray Chandler, Table of n, a(n) for n=1..38

Formula

{n: A138953(n)=A004086(n)} - R. J. Mathar, Jul 06 2009

Example

941 is in the list because 94 + 41 + 9 + 4 + 1 = 149.
51070 is in the list because 5107+1070+510+107+070+51+10+07+70+5+1+0+7+0=07015.

Crossrefs

Cf. A125303 (substrings without multiplicity). - R. J. Mathar, Jul 06 2009

Sequence in context: A332046 A166511 A062237 * A371462 A033022 A031497

Adjacent sequences: A162464 A162465 A162466 * A162468 A162469 A162470

Keyword

nonn,base

Author

Claudio Meller, Jul 04 2009

Extensions

Keyword base added, 10 to 90 and 147970 added by R. J. Mathar, Jul 06 2009

0 and a(16)-a(38) from Ray Chandler, Jul 15 2009

Status

approved