A038619 Smallest positive number that needs more lines when shown on a 7-segment display (digital clock) than any previous term.

1, 2, 6, 8, 10, 18, 20, 28, 68, 88, 108, 188, 200, 208, 288, 688, 888, 1088, 1888, 2008, 2088, 2888, 6888, 8888, 10888, 18888, 20088, 20888, 28888, 68888, 88888, 108888, 188888, 200888, 208888, 288888, 688888, 888888, 1088888, 1888888, 2008888, 2088888, 2888888, 6888888, 8888888

Offset

1,2

Comments

For n > 1, a(n) uses n + 3 segments to be displayed, when a digit '6' uses 6 segments (as in A234691, A234692 and A277116, A074458, A006942, A010371, but not in A063720). Sequence A143617 is the same but starts with 0, 8, ... and A216261 has additional terms 7 & 4 before 2 and 22 before 20. - M. F. Hasler, Jun 23 2020

Links

Table of n, a(n) for n=1..45.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,10,-10).

Formula

For n >= 3, the terms with n digits are given by: 108*A + B, 188*A + B, 200*A + B, 208*A + B, 288*A + B, 688*A + B, 888*A + B where A = 10^(n-3), B = 8*(A - 1)/9.

From M. F. Hasler, Jun 23 2020: (Start)

a(n) = 10*a(n-7) + 8 for n > 13 (and with a(n-6) for 7 < n < 13).

G.f.: (1 + x + 4*x^2 + 2*x^3 + 2*x^4 + 8*x^5 + 2*x^6 - 2*x^7 + 30*x^8 - 20*x^9 + 60*x^11 - 68*x^12 - 12*x^13)/((1 - x)*(1 - x^10)).

(End)

a(n) = a(n-1) + 10*a(n-7) - 10*a(n-8), for n >= 15. - Wesley Ivan Hurt, Jun 29 2020

Example

Digits 0, 1, 2, ..., 9 use 6, 2, 5, 5, 4, 5, 6, 3, 7, 6 lines / segments.

Mathematica

Block[{f, s}, MapIndexed[(f[#2[[1]] - 1] = #1) &, {6, 2, 5, 5, 4, 5, 6, 3, 7, 6}]; s = Array[Total[f /@ IntegerDigits[#]] &, 10^7]; Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* or *)
Nest[Append[#1, If[#2 > 13, 10 #1[[-7]] + 8, 10 #1[[-6]] + Boole[#2 != 13] 8]] & @@ {#, Length@ # + 1} &, {1, 2, 6, 8, 10, 18, 20}, 36] (* Michael De Vlieger, Jun 23 2020 *)

Prog

(PARI) apply( {A038619(n)=if(n>7, self()(n-6-(n>13))*10+(n!=13)*8, [1, 2, 6, 8, 10, 18, 20][n])}, [1..33]) \\ M. F. Hasler, Jun 23 2020

Crossrefs

Cf. A143617, A216261; A234691, A234692; A277116, A074458, A006942, A010371, A063720.

Sequence in context: A324175 A358428 A084909 * A118257 A378029 A066762

Adjacent sequences: A038616 A038617 A038618 * A038620 A038621 A038622

Keyword

nonn,base,easy,nice

Author

Jan Kristian Haugland

Extensions

Edited and offset corrected to 1 by M. F. Hasler, Jun 23 2020

More terms from Michael De Vlieger, Jun 23 2020

More terms from M. F. Hasler, Jun 23 2020

Status

approved