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A038619 Smallest positive number that needs more lines when shown on a 7-segment display (digital clock) than any previous term. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A302658 A324175 A084909 * A118257 A066762 A066198

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

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Last modified February 25 12:53 EST 2021. Contains 341607 sequences. (Running on oeis4.)