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A368077 Numbers k such that row k of Pascal's triangle mod 10 contains all the numbers 0 to 9.

%I A368077 #14 May 01 2025 13:24:08
%S A368077 47,59,89,94,117,118,119,123,147,173,189,198,214,219,221,222,223,233,
%T A368077 237,238,239,243,244,247,248,297,298,309,313,317,318,319,323,339,344,
%U A368077 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 A368077 Numbers k such that row k of Pascal's triangle mod 10 contains all the numbers 0 to 9.
%C A368077 Numbers k such that A208280(k) = 10.
%H A368077 Robert Israel, <a href="/A368077/b368077.txt">Table of n, a(n) for n = 1..10000</a>
%e A368077 a(3) = 89 is a term because
%e A368077   binomial(89,15) = 38163061637050680 == 0 (mod 10),
%e A368077   binomial(89,0) = 1 == 1 (mod 10),
%e A368077   binomial(89,5) = 41507642 == 2 (mod 10),
%e A368077   binomial(89,8) = 70625252863 == 3 (mod 10),
%e A368077   binomial(89,3) = 113564 == 4 (mod 10),
%e A368077   binomial(89,16) = 176504160071359395 == 5 (mod 10),
%e A368077   binomial(89,2) = 3916 == 6 (mod 10),
%e A368077   binomial(89,9) = 635627275767 == 7 (mod 10),
%e A368077   binomial(89,6) = 581106988 == 8 (mod 10), and
%e A368077   binomial(89,1) = 89 == 9 (mod 10).
%p A368077 filter:= proc(n) local k,S;
%p A368077   S:= {$0..9}:
%p A368077   for k from 0 to n/2 do
%p A368077     S:= S minus {(binomial(n,k) mod 10)};
%p A368077     if S = {} then return true fi
%p A368077   od;
%p A368077   false
%p A368077 end proc:
%p A368077 select(filter, [$1..1000]); # _Robert Israel_, Dec 10 2023
%o A368077 (Python)
%o A368077 from itertools import count, islice
%o A368077 def A368077_gen(): # generator of terms
%o A368077     a, b = [], set(range(10))
%o A368077     for i in count(0):
%o A368077         c, d = 0, []
%o A368077         for k in a:
%o A368077             d.append((c+k)%10)
%o A368077             c = k
%o A368077         a = d+[1]
%o A368077         if b.issubset(set(a)): yield i
%o A368077 A368077_list = list(islice(A368077_gen(),30)) # _Chai Wah Wu_, May 01 2025
%Y A368077 Cf. A208280.
%K A368077 nonn,base
%O A368077 1,1
%A A368077 _Robert Israel_, Dec 10 2023