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

4, 22, 94, 142, 262, 334, 358, 694, 862, 934, 1174, 1678, 1822, 2182, 2854, 3022, 3862, 3958, 4054, 4702, 4894, 5062, 5398, 5854, 6022, 6238, 6382, 6694, 7534, 7558, 7822, 8038, 8422, 9502, 9934, 10078, 10342, 10558, 11062, 11758, 12574, 12622, 13942, 14038, 14254, 14374, 15094, 16438, 16462

Offset: 1

Author

David Lovler, Jan 30 2021

Keywords

• nonn

Comments

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

Links

• David Lovler, Table of n, a(n) for n = 1..852

Crossrefs

Cf. A307002, A322744, A345357, A345473, A345474.

Programs

PARI

T319929(n, k) = if (n%2, if (k%2, n+k-1, k), if (k%2, n, 0));
T(n, k) = (3*n*k - T319929(n, k))/2; \\ A322744
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
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