cp's OEIS Frontend

A380550 List of numbers not of the form i + 3*j + 4*i*j for i, j >= 1.

%I A380550 #14 Jan 31 2025 04:23:23
%S A380550 1,2,3,4,5,6,7,9,10,11,12,14,16,17,19,20,21,25,26,27,30,31,32,34,37,
%T A380550 39,40,41,44,45,47,49,52,54,55,56,59,62,65,66,67,70,72,75,76,77,81,82,
%U A380550 84,86,89,91,94,95,102,104,107,109,110,111,115,116,117,119,121,122,124,125,129,130,135,136,140,142,144,146,147,149
%N A380550 List of numbers not of the form i + 3*j + 4*i*j for i, j >= 1.
%C A380550 This is a companion sequence to A380572. It is the complementary sequence to A380549.
%C A380550 Compare with A006093, numbers not of the form i + j + i*j, and A005097, numbers not of the form i + j + 2*i*j.
%C A380550 Apart from a(6) = 6, this sequence consists of all the positive integers N such that 4*N + 3 is either a prime or three times a prime.
%H A380550 Peter Bala, <a href="/A380550/a380550.pdf">4*A380550(n) + 3 is either a prime or three times a prime except when n = 6</a>
%e A380550 Factorization of 4*a(n) + 3 for n = 1..78:
%e A380550 [7,  11, 3*5, 19, 23, 3^3, 31, 3*13, 43, 47, 3*17, 59, 67, 71, 79, 83, 3*29, 103, 107, 3*37, 3*41, 127, 131, 139, 151, 3*53, 163, 167, 179, 3*61, 191, 199, 211, 3*73, 223, 227, 239, 251, 263, 3*89, 271, 283, 3*97, 3*101, 307, 311, 3*109, 331, 3*113, 347, 359, 367, 379, 383, 3*137, 419, 431, 439, 443, 3*149, 463, 467, 3*157, 479, 487, 491, 499, 503, 3*173, 523, 3*181, 547, 563, 571, 3*193, 587, 3*197, 599]
%p A380550 L := 150: N := {seq(n, n= 1..L)}: S := {}:
%p A380550 for i from 1 to L do
%p A380550   for j from 1 to L do
%p A380550     if i + 3*j + 4*i*j <= L then S := `union`(S, {i+3*j+4*i*j}) end if
%p A380550   end do;
%p A380550 end do:
%p A380550 N minus S;
%Y A380550 Cf. A005097, A006093, A380549, A380572.
%K A380550 nonn,easy
%O A380550 1,2
%A A380550 _Peter Bala_, Jan 26 2025