OFFSET
1,1
COMMENTS
The sequence is complete. In general, a number x = x_1 x_2 ... x_n of n digits belongs to the sequence if its digits satisfy a certain Diophantine equation c_1*x_1 + c_2*x_2 + ... + c_n*x_n = 0, where the coefficients c_i depend on n. It is easy to verify that for n > 11 all the coefficient c_i are positive, so the equation does not admit a nonzero solution. - Giovanni Resta, Jul 20 2015
FORMULA
For a number with n digits there are n substrings generated by removing one digit from the original number. So for 12345, these are 2345, 1345, 1245, 1235, 1234. Sum(x) is defined as the sum of these substrings for a number x and the sequence above is those numbers such that sum(x) = x.
EXAMPLE
First term is 1729404 because sum(1729404) = 729404 + 129404 + 179404 + 172404 + 172904 + 172944 + 172940 = 1729404.
PROG
(PARI) isok(n)=d = digits(n); if (sumdigits(n)*(#d-2) % 9 , return (0)); s = 0; for (i=1, #d, nd = vector(#d-1, j, if (i > j, d[j], d[j+1])); s += subst(Pol(nd), x, 10); ); s == n; \\ Michel Marcus, Apr 24 2014
CROSSREFS
KEYWORD
base,easy,nonn,full,fini
AUTHOR
Jon Ayres (jonathan.ayres(AT)ntlworld.com), Sep 05 2007
EXTENSIONS
a(12)-a(22) from Donovan Johnson, Jan 16 2011
a(23)-a(41) from Anthony Sand, Apr 24 2014
STATUS
approved