A316858 - OEIS

%I #24 Jul 15 2018 12:54:54

%S 6,8,8,10,10,10,6,12,12,6,14,8,14,8,14,16,16,10,10,16,16,6,18,18,6,18,

%T 18,6,20,8,20,14,14,20,8,20,22,22,10,16,22,16,10,22,22,6,24,24,6,24,

%U 24,6,24,24,6,26,8,26,20,14,26,14,20,26,8,26,8,28,10,22,28,16,16,28,22,10,28,8

%N Triangle read by rows constructed from A090368 as sum of least prime factors.

%C The greatest number in row k is 2*k + 4, thus consecutive rows identify consecutive even numbers (sums of two primes).

%C To get the n-th row: copy (1...n) of A090368, reverse, and add together.

%C When primes meet primes we get the maximum values. When primes or prime factors meet prime factors, we get lesser values. (Spot checked. Still empirical.)

%e Triangle begins:

%e { 6},         <--- copy (1,1) of A090368, add together

%e { 8,  8},     <--- copy (1,2) of A090368, reverse, and add together

%e {10, 10, 10}, <--- copy (1,3) of A090368, reverse, and add together

%e { 6, 12, 12,  6},

%e {14,  8, 14,  8, 14},

%e {16, 16, 10, 10, 16, 16},

%e { 6, 18, 18,  6, 18, 18,  6}, <=== differences from A316859 begin here

%e {20,  8, 20, 14, 14, 20,  8, 20},

%e {22, 22, 10, 16, 22, 16, 10, 22, 22},

%e { 6, 24, 24,  6, 24, 24,  6, 24, 24,  6},

%e {26,  8, 26, 20, 14, 26, 14, 20, 26,  8, 26},

%e { 8, 28, 10, 22, 28, 16, 16, 28, 22, 10, 28,  8}

%t lpf[n_] := FactorInteger[2 n + 1][[1, 1]]; A090368 = Array[lpf, 12];

%t a = Flatten[Table[A090368[[1 ;; -n]] + Reverse[A090368[[1 ;; -n]]],

%t     {n, Length[A090368], 1, -1}]];

%Y Cf. A090368, A316859 (related triangle using gpfs).

%K nonn,tabl

%O 1,1

%A _Fred Daniel Kline_, Jul 15 2018