A006942 - OEIS

A006942

Number of segments used to represent n on calculator display, variant 5: digits '6', '7' and '9' use 6, 3 and 6 segments, respectively.
(Formerly M4049)

6, 2, 5, 5, 4, 5, 6, 3, 7, 6, 8, 4, 7, 7, 6, 7, 8, 5, 9, 8, 11, 7, 10, 10, 9, 10, 11, 8, 12, 11, 11, 7, 10, 10, 9, 10, 11, 8, 12, 11, 10, 6, 9, 9, 8, 9, 10, 7, 11, 10, 11, 7, 10, 10, 9, 10, 11, 8, 12, 11, 12, 8, 11, 11, 10, 11, 12, 9, 13, 12, 9, 5, 8, 8, 7, 8, 9

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

a(A216261(n)) = n and a(m) <> n for m < A216261(n). - Reinhard Zumkeller, Mar 15 2013

If we mark with * resp. ' the graphical representations which use more resp. less segments, we have the following variants:

A063720 (6', 7', 9'), A277116 (6*, 7', 9'), A074458 (6*, 7*, 9'),

_______________ this: A006942 (6*, 7', 9*), A010371 (6*, 7*, 9*).

Sequences A234691, A234692 and variants make precise which segments are lit in each digit. These are related through the Hamming weight function A000120, e.g., A010371(n) = A000120(A234691(n)) = A000120(A234692(n)). - M. F. Hasler, Jun 17 2020

REFERENCES

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file, Instructions problem series.31, and Series Section solution series.31.

Index entries for sequences related to calculator display

FORMULA

a(n) = a(floor(n/10)) + a(n mod 10) for n > 9. - Reinhard Zumkeller, Mar 15 2013

a(n) = A010371(n) - A102679(n) + A102681(n) (subtract the number of digits 7 in n) = A277116(n) + A102683(n) (add number of digits 9 in n); and in particular, A063720(n) <= A277116(n) <= a(n) = A010371(n). - M. F. Hasler, Jun 17 2020

EXAMPLE

As depicted below, zero uses 6 segments, so a(0)=6.

_ _ _ _ _ _ _ _

| | | _| _| |_| |_ |_ | |_| |_|

|_| | |_ _| | _| |_| | |_| _|

[Edited by Jon E. Schoenfield, Jul 30 2017]

MAPLE

A006942 := proc(n) local d, dig, j, s: if(n=0)then return 6:fi: dig:=[6, 2, 5, 5, 4, 5, 6, 3, 7, 6]: d:=convert(n, base, 10): s:=0: for j from 1 to nops(d) do s:=s+dig[d[j]+1]: od: return s: end: seq(A006942(n), n=0..100); # Nathaniel Johnston, May 08 2011

MATHEMATICA

MapIndexed[ (f[First[#2] - 1] = #1)& , {6, 2, 5, 5, 4, 5, 6, 3, 7, 6}]; a[n_] := Plus @@ f /@ IntegerDigits[n]; Table[a[n], {n, 0, 76}] (* Jean-François Alcover, Sep 25 2012 *)

a[n_] := Plus @@ (IntegerDigits@ n /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 7 -> 3, 8 -> 7, 9 -> 6}); Array[a, 77, 0] (* Robert G. Wilson v, Jun 20 2018 *)

PROG

(Haskell)

a006942 n = a006942_list !! n

a006942_list = [6, 2, 5, 5, 4, 5, 6, 3, 7, 6] ++ f 10 where

f x = (a006942 x' + a006942 d) : f (x + 1)

where (x', d) = divMod x 10

-- Reinhard Zumkeller, Mar 15 2013

(PARI) a(n)=if(n==0, return(6)); my(d=digits(n), v=vector(10)); for(i=1, #d, v[d[i]+1]++); v*[6, 2, 5, 5, 4, 5, 6, 3, 7, 6]~ \\ Charles R Greathouse IV, Feb 05 2018

(Python)

def a(n): return sum([6, 2, 5, 5, 4, 5, 6, 3, 7, 6][int(d)] for d in str(n))

print([a(n) for n in range(77)]) # Michael S. Branicky, Jun 02 2021

CROSSREFS

Cf. A216261 (least inverse), A165244 (sorted digits), A302552 (primes), A328330 (iterations), A331529 (histogram).

Variants are A010371, A063720, A074458, A277116, see comments.