cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A354430 First diagonal of an array, generated from the sequence of the nonprimes.

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%I A354430 #27 Jul 23 2022 19:23:50
%S A354430 1,7,22,58,142,334,766,1726,3837,8435,18364,39646,84986,181117,384160,
%T A354430 811676,1709425,3590213,7522354,15728427,32827027,68405533,142344708,
%U A354430 295824870,614046159,1273068141,2636250146,5452584131,11264148401,23242423457,47903544728
%N A354430 First diagonal of an array, generated from the sequence of the nonprimes.
%C A354430 Mirroring the idea in A048457, here with nonprimes, and including 1 of the first generation.
%C A354430 We write down the sequence of the nonprimes 1, 4, 6, ... in the first row of the array. Nonprime(k) + nonprime(k+2) will generate the second row. Thereafter we generate the further rows in a similar manner. The leftmost diagonal gives the sequence.
%H A354430 Michael S. Branicky, <a href="/A354430/b354430.txt">Table of n, a(n) for n = 1..3311</a>
%e A354430 1    4    6    8    9   10   12   14   15   16   18   20   21 ...
%e A354430      7   12   15   18   21   24   27   30   33   36   39 ...
%e A354430          22   30   36   42   48   54   60   66   72 ...
%e A354430               58   72   84   96  108  120  132 ...
%e A354430                   142  168  192  216  240 ...
%e A354430                        334  384  432 ...
%e A354430                             766 ...
%o A354430 (Python)
%o A354430 from sympy import composite
%o A354430 from functools import lru_cache
%o A354430 @lru_cache(maxsize=None)
%o A354430 def T(r, k):
%o A354430     if r == 1: return 1 if k == 1 else composite(k-1)
%o A354430     return T(r-1, k) + T(r-1, k+2)
%o A354430 def a(n): return T(n, 1)
%o A354430 print([a(n) for n in range(1, 30)]) # _Michael S. Branicky_, May 28 2022
%Y A354430 Cf. A001787, A018252, A048457, A048448, A099862.
%K A354430 nonn,easy
%O A354430 1,2
%A A354430 _Tamas Sandor Nagy_, May 27 2022
%E A354430 a(8) and beyond from _Michael S. Branicky_, May 28 2022