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 A275512 The consecutive sizes of the blocks of terms containing at least one digit "1" are given by the sequence itself. 1
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 12, 13, 14, 22, 15, 16, 17, 18, 23, 19, 21, 31, 41, 51, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 71, 81, 91, 100, 101, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence starts with a(1) = 1 and is extended with the smallest integer not yet used that does not lead to a contradiction. LINKS EXAMPLE The blocks of terms including at least a digit "1" are indicated here by parentheses; the successive block-sizes are 1, 2, 3, 4, 5,... which reproduces the sequence itself: (1),2,3,4,5,6,7,8,9,(10,11),20,(12,13,14),22,(15,16,17,18),23,(19,21,31,41,51),24... MAPLE isA011531 := proc(n)     nops(convert(convert(n, base, 10), set) intersect {1}) > 0 ;     simplify(%) ; end proc: A011531_next := proc(n)     local a;     for a from n+1 do         if isA011531(a) then             return a;         end if;     end do: end proc: isA052383 := proc(n)     not isA011531(n) ; end proc: A052383_next := proc(n)     local a;     for a from n+1 do         if isA052383(a) then             return a;         end if;     end do: end proc: A275512grp1 := proc(a)     local idx1, n ;     idx1 := 0 ;     if isA052383(a) then         return 0;     end if;     for n from 1 do         if isA011531(A275512(n)) then             if n =1 then                 idx1 := 1;             elif isA052383(A275512(n-1)) then                 idx1 := idx1+1 ;             end if;         end if;         if A275512(n) = a then             return idx1 ;         end if;     end do: end proc: A275512 := proc(n)     option remember;     local a, aprev, prev1, grp1, d, seen, reqlen, npr;     if n =1 then         1;     else         for a from 2 do             seen := false;             for npr from 1 to n-1 do                 if procname(npr) = a then                     seen := true;                     break;                 end if;             end do:             if not seen then                 aprev := procname(n-1) ;                 if isA052383(aprev) then                     return a;                 else                     prev1 := 0 ;                     for d from 1 to n-1 do                         if isA011531(procname(n-d)) then                             prev1 := prev1+1 ;                         else                             break;                         end if;                     end do:                     grp1 := A275512grp1(aprev) ;                     reqlen := procname(grp1) ;                     if reqlen > prev1 then                         return A011531_next(aprev) ;                     elif n-prev1-1 > 0 then                         return A052383_next(procname(n-prev1-1)) ;                     else                         return 2 ;                     end if;                 end if;             end if;         end do;     end if; end proc: seq(A275512(n), n=1..100) ; # R. J. Mathar, Jul 31 2016 CROSSREFS Cf. A011531, A052383. Sequence in context: A032980 A239217 A130571 * A303948 A275413 A273376 Adjacent sequences:  A275509 A275510 A275511 * A275513 A275514 A275515 KEYWORD nonn,base,less AUTHOR Eric Angelini, Jul 31 2016 STATUS approved

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)