A143617 Where record values occur in A010371.

0, 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

Offset: 1

Author

Reinhard Zumkeller, Aug 27 2008

Keywords

• nonn

Comments

a(n) is the least number using n + 6 (or n + 5 for n < 5) segments on a 7-segment display, when '6' uses 6 segments. This is essentially the same as A038619 (starts with 1, 2, 6 instead of 0) and A216261 (= a(n) uses n segments: has 4 values before 0 and 22 before 20). - M. F. Hasler, Jun 17 2020

Links

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

Crossrefs

Cf. A010371, A143616.

Programs

Mathematica

Block[{f, s}, MapIndexed[(f[#2[[1]] - 1] = #1) &, {6, 2, 5, 5, 4, 5, 6, 4, 7, 6}]; s = Array[Total[f /@ IntegerDigits[#]] &, 10^6, 0]; Map[-1 + FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Jun 23 2020 *)

PARI

apply( {A143617(n)=if(n>11,self()(n-7)*10+8, n>9, 12*n+68, n>6, 20*n-72, n*5-2-n%2*3)}, [1..55]) \\ M. F. Hasler, Jun 23 2020

Formula

a(n+7) = 10*a(n) + 8 for n > 4.

A010371(a(n)) = A143616(n) and A010371(m) < A143616(n) for m < a(n).

A010371(a(n)) = n + 6 for n > 4. - M. F. Hasler, Jun 23 2020

a(n) = a(n-1) + 10*a(n-7) - 10*a(n-8). - Wesley Ivan Hurt, Jul 03 2020