A117695 - OEIS

%I #20 May 12 2024 10:03:01

%S 0,0,1,1,2,2,3,3,4,4,4,4,5,5,6,6,7,7,8,9,8,8,9,9,10,10,11,11,12,13,12,

%T 12,13,13,14,14,15,15,16,18,16,16,17,17,18,18,19,19,20,22,20,20,21,21,

%U 22,22,23,23,24,27,24,24,25,25,26,26,27,27,28,31,28,28,29,29,30,30,31

%N a(n) is the number of pairs of distinct positive integers not containing a digit 0 giving a sum equal to n.

%H David A. Corneth, <a href="/A117695/b117695.txt">Table of n, a(n) for n = 1..10000</a>

%e 10 = 1 + 9 = 2 + 8 = 3 + 7 = 4 + 6 therefore we have 4 different couples.

%e 9 + 1 is not considered because it is the same couple as 1 + 9.

%e 5 + 5 is not considered because we consider couples with different numbers.

%p P:=proc(n)local i,j,k,cc,lm,ok,count; for cc from 1 by 1 to n do if trunc(cc/2)*2=cc then lm:=cc/2-1 else lm:=trunc(cc/2) fi; count:=0; for i from 1 by 1 to lm do ok:=0; k:=i; while k>0 do j:=frac(k/10)*10; if j=0 then ok:=1; fi; k:=trunc(k/10); od; k:=cc-i; while k>0 do j:=frac(k/10)*10; if j=0 then ok:=1; fi; k:=trunc(k/10); od; if ok=1 then count:=count+1; fi; od; print(lm-count); od; end: P(1000);

%o (PARI) iszerofree(n) = vecmin(digits(n)) > 0

%o a(n) = sum(i = 1, (n-1)\2, iszerofree(i) && iszerofree(n-i)) \\ _David A. Corneth_, May 12 2024

%Y Cf. A117644.

%K nonn,base

%O 1,5

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Apr 13 2006

%E Name edited and offset changed to 1 by _David A. Corneth_, May 12 2024