A119385 Write out the digits of the integers in order (cf. A007376): 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 ...; a(n) = sum of digits between successive zeros.

0, 46, 56, 66, 76, 86, 96, 106, 116, 126, 127, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 66, 76, 86, 96, 106, 116, 126, 136, 137, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 76, 86, 96, 106, 116, 126, 136, 146, 147, 0, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 86, 96, 106, 116, 126, 136, 146, 156, 157, 0, 4

Offset

0,2

Comments

a(0) = 0 by convention.

Links

Table of n, a(n) for n=0..72.

Maple

c:=proc(x, y) local s: s:=proc(m) nops(convert(m, base, 10)) end: if y=0 then 10*x else x*10^s(y)+y: fi end: b:=proc(n) local nn: nn:=convert(n, base, 10): [seq(nn[nops(nn)+1-i], i=1..nops(nn))] end: A:=0: for n from 1 to 500 do A:=c(A, n) od: B:=[0, seq(b(A)[j], j=1..nops(b(A)))]: u:=proc(n) if B[n]=0 then n else fi end: U:=[seq(u(n), n=1..nops(B))]: 0, seq(add(B[j], j=U[i]..U[i+1]), i=1..nops(U)-1); # there must exist a simpler Maple program! - Emeric Deutsch, Jul 27 2006
#alternative
A119385 := proc(n) option remember ; local nupto, a, a007376, k ; if n =0 then RETURN([0, 0]) ; else nupto := op(2, A119385(n-1)) ; a := 0 ; for k from nupto+1 do a007376 := A007376(k) ; if op(1, a007376) > 0 then a := a+op(1, a007376) ; else RETURN([a, k]) ; fi ; od: fi ; end :# R. J. Mathar, Jan 21 2008

Mathematica

list1=Flatten[Table[IntegerDigits[i], {i, 0, 1000}]];
index1=Partition[Flatten[Position[list1, 0]], 2, 1];
Plus@@@Table[Take[list1, Flatten[Take[index1, {i}]]], {i, Length[index1]}] (From Harvey Dale)

Crossrefs

Sequence in context: A363762 A336098 A115444 * A330243 A326646 A332952

Adjacent sequences: A119382 A119383 A119384 * A119386 A119387 A119388

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Jul 26 2006

Extensions

More terms from Emeric Deutsch, Jul 27 2006

Status

approved