A368077 - OEIS

%I #8 Dec 30 2023 23:13:28

%S 47,59,89,94,117,118,119,123,147,173,189,198,214,219,221,222,223,233,

%T 237,238,239,243,244,247,248,297,298,309,313,317,318,319,323,339,344,

%U 345,346,347,348,363,366,367,368,369,373,397,398,409,413,414,417,418,421,422,423,429,433,437,438,439

%N Numbers k such that row k of Pascal's triangle mod 10 contains all the numbers 0 to 9.

%C Numbers k such that A208280(k) = 10.

%H Robert Israel, <a href="/A368077/b368077.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 89 is a term because

%e   binomial(89,15) = 38163061637050680 == 0 (mod 10),

%e   binomial(89,0) = 1 == 1 (mod 10),

%e   binomial(89,5) = 41507642 == 2 (mod 10),

%e   binomial(89,8) = 70625252863 == 3 (mod 10),

%e   binomial(89,3) = 113564 == 4 (mod 10),

%e   binomial(89,16) = 176504160071359395 == 5 (mod 10),

%e   binomial(89,2) = 3916 == 6 (mod 10),

%e   binomial(89,9) = 635627275767 == 7 (mod 10),

%e   binomial(89,6) = 581106988 == 8 (mod 10), and

%e   binomial(89,1) = 89 == 9 (mod 10).

%p filter:= proc(n) local k,S;

%p   S:= {$0..9}:

%p   for k from 0 to n/2 do

%p     S:= S minus {(binomial(n,k) mod 10)};

%p     if S = {} then return true fi

%p   od;

%p   false

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Dec 10 2023

%Y Cf. A208280.

%K nonn,base

%O 1,1

%A _Robert Israel_, Dec 10 2023