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A216587
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Preimage of n for A216556 (i.e., concatenation of digits of a(n), each increased by 1, yields n), -1 if there is none.
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5
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-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 11, 12, 13, 14, 15, 16, 17, 18, -1, 20, 21, 22, 23, 24, 25, 26, 27, 28, -1, 30, 31, 32, 33, 34, 35, 36, 37, 38, -1, 40, 41, 42, 43, 44, 45, 46, 47, 48, -1, 50, 51, 52, 53, 54, 55, 56, 57, 58, -1, 60, 61, 62, 63
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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Sequence A216589 lists the indices n for which a(n)=-1, i.e., n is not in the range of A216556.
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LINKS
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FORMULA
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a(n)=n-1 for n < 11; a(n)=n-11 for 20 < n < 110 except n=30, 40, ..., 100.
a(n)=-1 if n contains a substring "20", "30",..., "90" or "00", or if n starts with digits "11", "12", ..., "19". For all other n>1 one has a(n)>0.
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EXAMPLE
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a(a(a(2127)))=a(a(1016))=a(905)=-1, since under A216556, 905 -> 1016 -> 2127, but no n yields A216556(n)=905.
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PROG
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(PARI) A216587(n)={my(s=0); n!=1&for(i=1, #n=Vecsmall(Str(n)), n[i]>48||(i>1&n[i-1]==49&s=s\10+1)||return(-1); (s=s*10+n[i]-49)&next; (i<#n&n[i++]==48&s=9)||return(-1)); s}
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CROSSREFS
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KEYWORD
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sign,base,easy
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AUTHOR
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STATUS
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approved
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