A316858 Triangle read by rows constructed from A090368 as sum of least prime factors.

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

Offset: 1

Author

Fred Daniel Kline, Jul 15 2018

Keywords

• nonn
• tabl

Comments

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

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

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.)

Examples

			Triangle begins:
{ 6},         <--- copy (1,1) of A090368, add together
{ 8,  8},     <--- copy (1,2) of A090368, reverse, and add together
{10, 10, 10}, <--- copy (1,3) of A090368, reverse, and add together
{ 6, 12, 12,  6},
{14,  8, 14,  8, 14},
{16, 16, 10, 10, 16, 16},
{ 6, 18, 18,  6, 18, 18,  6}, <=== differences from A316859 begin here
{20,  8, 20, 14, 14, 20,  8, 20},
{22, 22, 10, 16, 22, 16, 10, 22, 22},
{ 6, 24, 24,  6, 24, 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}
		

Crossrefs

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

Programs

Mathematica

lpf[n_] := FactorInteger[2 n + 1][[1, 1]]; A090368 = Array[lpf, 12];
a = Flatten[Table[A090368[[1 ;; -n]] + Reverse[A090368[[1 ;; -n]]],
    {n, Length[A090368], 1, -1}]];