The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A332584 a(n) = minimal value of n+k (with k >= 1) such that the concatenation of the decimal digits of n,n+1,...,n+k is divisible by n+k+1, or -1 if no such n+k exists. 7
 2, 82, 1888, 6842, 6, 50, 20, 10, 1320, 28, 208, 32, 66, 148, 1008, 60, 192, 124536, 282, 46, 128, 32, 28, 86, 40, 33198, 36, 42, 346, 738, 1532, 246, 70, 68, 102, 306, 56, 20226, 78316, 10778, 328, 2432, 738 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Certainly a(n) must be even, since no odd number can be divisible by an even number. The values of k = a(n)-n are given in the companion sequence A332580, which also has an extendedtable of values. A heuristic argument suggests that n+k should always exist. LINKS J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], April 2020. FORMULA a(n) = n + A332580(n) (trivially from the definitions). EXAMPLE a(1) = 2 as '1' || '2' = '12', which is divisible by 3 (where || denotes decimal concatenation). a(7) = 20 as '7' || '8' || '9' || '10' || '11' || '12' || ... || '20' = 7891011121314151617181920, which is divisible by 21. a(8) = 10 as '8' || '9' || '10' = 8910, which is divisible by 11. a(2) = 82: the concatenation 2 || 3 || ... || 82 is   23456789101112131415161718192021222324252627282930313233343536373839\   40414243444546474849505152535455565758596061626364656667686970717273747\   576777879808182, which is divisible by 83. MAPLE grow := proc(n, M) # searches out to a limit of M, returns [n, n+k] or [n, -1] if no k was found local R, i; R:=n; for i from n+1 to M do R:=R*10^length(i)+i; if (i mod 2) = 0 then if (R mod (i+1)) = 0 then return([n, i]); fi; fi; od: [n, -1]; end; for n from 1 to 100 do lprint(grow(n, 20000)); od; PROG (PARI) apply( {A332584(n, L=10^#Str(n), c=n)= until((c=c*L+n)%(n+1)==0, n++

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 09:03 EDT 2020. Contains 337298 sequences. (Running on oeis4.)