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A340748 Numbers m > 3 such that m-1, m, m+1 belong to A307002.

%I A340748 #39 Dec 15 2021 02:32:06
%S A340748 4,22,94,142,262,334,358,694,862,934,1174,1678,1822,2182,2854,3022,
%T A340748 3862,3958,4054,4702,4894,5062,5398,5854,6022,6238,6382,6694,7534,
%U A340748 7558,7822,8038,8422,9502,9934,10078,10342,10558,11062,11758,12574,12622,13942,14038,14254,14374,15094,16438,16462
%N A340748 Numbers m > 3 such that m-1, m, m+1 belong to A307002.
%C A340748 All terms m == 1 (mod 3). To prove this, look at gaps of 3 in row 2 of array A322744(n,k). The longest strings of consecutive numbers not in A322744(n,k) can occur only for these 3 numbers. The number following such a gap is A322744(2,e) = (3*2*e)/2 = 3e for some even e. The middle of the string, m = A322744(2,e) - 2 = 3e - 2. Thus m == 1 (mod 3). After the first term, all terms m == 2 (mod 4).- _David Lovler_, Nov 29 2021
%H A340748 David Lovler, <a href="/A340748/b340748.txt">Table of n, a(n) for n = 1..852</a>
%o A340748 (PARI) T319929(n, k) = if (n%2, if (k%2, n+k-1, k), if (k%2, n, 0));
%o A340748 T(n, k) = (3*n*k - T319929(n, k))/2; \\ A322744
%o A340748 list(nn) = {my(list = List()); for (n=2, nn, for (k=2, nn\n, listput(list, T(n, k)); ); ); setminus([1..nn], Set(list)); } \\ A307002
%o A340748 lista(nn) = {my(v=Vec(list(nn))); for (m=4, #v-1, my(x=v[m]); if (vecsearch(v, x-1) && vecsearch(v, x+1), print1(x, ", ")););} \\ _Michel Marcus_, Apr 02 2021
%Y A340748 Cf. A307002, A322744, A345357, A345473, A345474.
%K A340748 nonn
%O A340748 1,1
%A A340748 _David Lovler_, Jan 30 2021