

A216261


Smallest positive number using exactly n segments on a calculator display (when '6' and '7' are represented using 6 resp. 3 segments).


7



1, 7, 4, 2, 0, 8, 10, 18, 22, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,2


COMMENTS

Essentially the same as A038619 and A143617. One could argue that a(3) should rather be 1 (prior to adding "positive" in the definition), which does use 3 segments on typical 7segment displays, and is smaller than 7. Also, most pocket calculators and the Unicode standard (cf. links) use 4 rather than 3 segments to represent a '7' (as in A074458 and A010371, rather than A063720, A277116 or A006942), in which case a(3) is undefined if negative numbers are not allowed. No digit '9' will ever occur here, whether it would be represented with 6 or only 5 segments. However, digit '6' does occur, as the second smallest digit using 6 segments as does '0', which cannot occur as leading digit. If '6' is represented with 5 segments, any prefix 68 would be replaced with 80.  M. F. Hasler and Kevin Ryde, Jun 17 2020


LINKS

Table of n, a(n) for n=2..47.
Unicode, Symbols for Legacy Computing, The Unicode Standard, Version 13.0, 2020.
Index entries for sequences related to calculator display
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,10,10).


FORMULA

A006942(a(n)) = n and A006942(m) <> n for m < a(n).
a(n+7) = 10*a(n) + 8 for n > 10. This can be deduced from a(n) = min{10*a(nA006942(r))+r, r=0..9} via strong induction.  David Radcliffe, Jan 29 2016
G.f.: (x^2 +6*x^3 3*x^4 2*x^5 2*x^6 +8*x^7 +2*x^8 2*x^9 56*x^10 +28*x^11 +28*x^12 +60*x^13 60*x^14 28*x^17 +28*x^18)/((1x)*(110*x^7)).  David Radcliffe, Jan 29 2016


MATHEMATICA

Drop[#, 2] &@ CoefficientList[Series[(x^2 + 6 x^3  3 x^4  2 x^5  2 x^6 + 8 x^7 + 2 x^8  2 x^9  56 x^10 + 28 x^11 + 28 x^12 + 60 x^13  60 x^14  28 x^17 + 28 x^18)/((1  x) (1  10 x^7)), {x, 0, 50}], x] (* Michael De Vlieger, Jan 29 2016 *)


PROG

(Haskell)
import Data.Maybe (fromJust)
import Data.List (elemIndex)
a216261 = fromJust . (`elemIndex` a006942_list)
 Reinhard Zumkeller, Mar 15 2013
(PARI) Vec((x^2 +6*x^3 3*x^4 2*x^5 2*x^6 +8*x^7 +2*x^8 2*x^9 56*x^10 +28*x^11 +28*x^12 +60*x^13 60*x^14 28*x^17 +28*x^18)/((1x)*(110*x^7)) + O(x^50)) \\ Michel Marcus, Jan 29 2016


CROSSREFS

Cf. A006942, A010371, A063720, A074458, A277116; A234691, A234692.
Cf. A038619 and A143617 (identical up to initial terms).
Sequence in context: A187056 A103240 A155531 * A188628 A021578 A273093
Adjacent sequences: A216258 A216259 A216260 * A216262 A216263 A216264


KEYWORD

nonn,base


AUTHOR

Reinhard Zumkeller, Mar 15 2013


EXTENSIONS

Name and crossreferences edited by M. F. Hasler, Jun 17 2020


STATUS

approved



