cp's OEIS Frontend

A219840 Irregular triangle R(n,k) = n mod A000040(k), for 1 <= k <= i, where i is the least such that n < A002110(i).

%I A219840 #20 Sep 08 2022 08:46:04
%S A219840 1,0,2,1,0,0,1,1,2,0,0,1,1,1,2,0,2,3,1,0,4,0,1,0,1,2,1,0,0,2,1,1,3,0,
%T A219840 2,4,1,0,0,0,1,1,1,2,2,0,0,3,1,1,4,0,2,0,1,0,1,0,1,2,1,2,3
%N A219840 Irregular triangle R(n,k) = n mod A000040(k), for 1 <= k <= i, where i is the least such that n < A002110(i).
%C A219840 By the Chinese Remainder Theorem, x = n is the unique, for 0 <= m < A002110(i), solution to the set of congruences x = R(n,k) (mod A000040(k)), for 1 <= k <= i.
%H A219840 Jason Kimberley, <a href="/A219840/b219840.txt">Rows n = 1..2310 of irregular triangle, flattened</a>
%e A219840 1:  1;
%e A219840 2:  0, 2;
%e A219840 3:  1, 0;
%e A219840 4:  0, 1;
%e A219840 5:  1, 2;
%e A219840 6:  0, 0, 1;
%e A219840   ...
%e A219840 29: 1, 2, 4;
%e A219840 30: 0, 0, 0, 2;
%e A219840   ...
%e A219840 209:1, 2, 4, 6;
%e A219840 210:0, 0, 0, 0, 1;
%o A219840 (Magma) A002110 := func<n|&*[Integers()|NthPrime(j):j in[1..n]]>;
%o A219840 A219840_block := func<i|[[n mod NthPrime(k):k in[1..i]]:n in[A002110(i-1)..A002110(i)-1]]>;
%o A219840 [A219840_block(i):i in[1..4]];
%Y A219840 The n-th row of this sequence is the length i prefix of the n-th row of A147693.
%K A219840 nonn,easy,tabf
%O A219840 1,3
%A A219840 _Jason Kimberley_, Nov 29 2012