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 A234512 Numbers n = d(0)d(1)d(2)...d(r) such that d(i) is the number of differences |d(i)-d(i-1)| equal to i in n, i = 1,2,...,r. 1
 110, 311000, 2301000, 3003000, 3120000, 42100000, 410300000, 430100000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In the decimal system a differential autobiographical number is a natural number such that d(0) is the number of differences |d(i)-d(i-1)| = 0, d(1) is the number of differences |d(i)-d(i-1)| = 1, and so on. Property of this sequence: the sum of the decimal digits of a(n) equals length(a(n))-1. It is possible to extend this problem by counting the differences |d(i)-d(i-1)| with the additional difference |d(r)-d(1)|. So we find a new sequence b(n) = 22100, 311100, 3022000, 20402000, 31310000, 40004000, 422010000, 430110000 with the property that the sum of the decimal digits of b(n) equals length(b(n)). LINKS Tanya Khovanova, Autobiographical Numbers EXAMPLE 311000 is in the sequence because the differential digits are: |1-3| = 2; |1-1| = 0; |0-1| = 1; |0-0| = 0; |0-0| = 0, and 0 appears three times => 3; 1 appears one time => 1; 2 appears one time  => 1; 3 appears zero time => 0; 4 appears zero time => 0; 5 appears zero time => 0, hence a(2) = 311000. MAPLE with(numtheory):for n from 10 to 10^10 do:T:=array(0..9):for k from 0 to 9 do:T[k]:=0:od:x:=convert(n, base, 10):n1:=nops(x):for i from 1 to n1-1 do:a:=abs(x[i]-x[i+1]):T[a]:=T[a]+1:od:s:=sum('T[i]*10^(10-i-1)', 'i'=0..9): for u from 9 by -1 to 1 do:if T<>0 and irem(s, 10^u)=0 and s/10^u = n then print(n):else fi:od:od: CROSSREFS Cf. A037904, A046043, A108551, A138480. Sequence in context: A203718 A143750 A192844 * A343181 A028673 A138280 Adjacent sequences:  A234509 A234510 A234511 * A234513 A234514 A234515 KEYWORD nonn,base,fini AUTHOR Michel Lagneau, Dec 27 2013 STATUS approved

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Last modified June 26 04:58 EDT 2022. Contains 354877 sequences. (Running on oeis4.)