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.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• base
• nonn
• nice
• easy

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

Examples

			As depicted below, zero uses 6 segments, so a(0)=6.
   _     _  _       _   _   _   _   _
  | | |  _| _| |_| |_  |_    | |_| |_|
  |_| | |_  _|   |  _| |_|   | |_|  _|
.
[Edited by _Jon E. Schoenfield_, Jul 30 2017]
		

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

Crossrefs

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

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

See also A234691, A234692, A000120.

Programs

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

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 *)

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

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

Extensions

More terms from Matthew Conroy, Sep 13 2001