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%I #10 May 16 2020 12:04:49
%S 12,34,567,8,910,111213141516,17181920,2122232425262728,293031,
%T 323334353637383940,41424344454647,48,
%U 49505152535455565758596061626364,6566,676869707172737475,767778798081828384,85,868788
%N Partition the concatenation 1234567...of natural numbers into successive strings nontrivially (a(n) is not equal to n) such that the n-th string is a multiple of n.
%C a(1) = 12, a(n) = smallest concatenation of next successive natural numbers that is a multiple of n, or 0 if no such concatenation exists.
%C a(1) = 1 would have given a trivial sequence 1,2,3,4,5....
%C Every partial concatenation is a left substring of the concatenation of natural numbers.
%F a(n) = A077294(n)*n. - _Jinyuan Wang_, May 16 2020
%e a(2) = 34 = 2*17; a(7) = 17181920 = 7*2454560.
%o (PARI) lista(nn) = {my(k=0, m); for(n=1, nn, m=k++; while(m%n>0 || m==n, m=eval(Str(m, k++))); print1(m, ", ")); } \\ _Jinyuan Wang_, May 16 2020
%Y Cf. A077294, A088597, A088598.
%K nonn,base
%O 1,1
%A _Amarnath Murthy_, Nov 03 2002
%E Corrected and extended by _Ray Chandler_, Oct 18 2003
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