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

1,1

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.)

Links

Table of n, a(n) for n=1..78.

Example

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}

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}]];

Crossrefs

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

Sequence in context: A229020 A113697 A154476 * A316859 A185200 A216275

Adjacent sequences: A316855 A316856 A316857 * A316859 A316860 A316861

Keyword

nonn,tabl

Author

Fred Daniel Kline, Jul 15 2018

Status

approved