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Revision History for A131639

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Showing entries 1-10 | older changes
Numbers n such that the sum of all numbers formed by deleting one digit from n is equal to n.
(history; published version)
#25 by N. J. A. Sloane at Thu Nov 16 15:52:23 EST 2017
COMMENTS

The sequence is finite and fullcomplete. 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

Discussion
Thu Nov 16
15:52
OEIS Server: https://oeis.org/edit/global/2714
#24 by Charles R Greathouse IV at Wed May 04 13:22:55 EDT 2016
STATUS

editing

approved

#23 by Charles R Greathouse IV at Wed May 04 13:22:49 EDT 2016
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

AUTHOR

Jon Ayres (jonathan.ayres(AT)ntlworld.com), Sep 05 2007

STATUS

approved

editing

Discussion
Wed May 04
13:22
Charles R Greathouse IV: Fixing old email.
#22 by Jon E. Schoenfield at Sun Aug 09 23:37:20 EDT 2015
STATUS

editing

approved

#21 by Jon E. Schoenfield at Sun Aug 09 23:37:18 EDT 2015
COMMENTS

The sequence is finite and full. 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 non-zero nonzero solution. - Giovanni Resta, Jul 20 2015

STATUS

approved

editing

#20 by Bruno Berselli at Mon Jul 20 08:54:15 EDT 2015
STATUS

proposed

approved

#19 by Giovanni Resta at Mon Jul 20 08:48:14 EDT 2015
STATUS

editing

proposed

#18 by Giovanni Resta at Mon Jul 20 08:47:30 EDT 2015
COMMENTS

The sequence is finite and full. 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 non-zero solution. - Giovanni Resta, Jul 20 2015

KEYWORD

base,easy,nonn,full,fini

STATUS

approved

editing

#17 by N. J. A. Sloane at Sat May 03 13:16:11 EDT 2014
STATUS

proposed

approved

#16 by Michel Marcus at Wed Apr 30 18:19:38 EDT 2014
STATUS

editing

proposed