

A306196


Irregular triangle read by rows where row n lists the primes 2n  k, with 1 < k < 2n1, and if k is composite also 2n  p has to be prime for some prime divisor p of k.


0



2, 3, 2, 3, 5, 3, 5, 7, 2, 5, 7, 2, 3, 5, 7, 11, 3, 5, 7, 11, 13, 3, 5, 7, 11, 13, 2, 3, 5, 7, 11, 13, 17, 2, 3, 5, 7, 11, 13, 17, 19, 2, 3, 5, 7, 11, 13, 17, 19, 2, 3, 5, 7, 11, 13, 17, 19, 23, 3, 5, 11, 13, 17, 23, 2, 7, 11, 13, 17, 19, 23, 2, 3, 5, 11, 13, 17, 19, 23, 29
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

Conjectures:
(i) 1 <= A035026(n) <= (nth row length of this triangle) for n >= 2;
(ii) a(n,1) < A171637(n,1) for n >= 4.
Numbers m such that mth row length of this triangle is equal to A000720(m): 1, 2, 11, 13, 25, 56, 60, ...


LINKS



EXAMPLE

Row 2 = [2] because 2*2 = 2 + 2;
Row 3 = [3] because 2*3 = 3 + 3;
Row 4 = [2,3,5] because 2*4  2 = 6 = 2*3 and 2*4 = 3 + 5;
Row 5 = [3,5,7} because 2*5 = 3 + 7 = 5 + 5.
The table starts:
2;
3;
2, 3, 5;
3, 5, 7;
2, 5, 7;
2, 3, 5, 7, 11;
3, 5, 7, 11, 13;
3, 5, 7, 11, 13;
2, 3, 5, 7, 11, 13, 17;
2, 3, 5, 7, 11, 13, 17, 19;
2, 3, 5, 7, 11, 13, 17, 19;
2, 3, 5, 7, 11, 13, 17, 19, 23;
3, 5, 11, 13, 17, 23;
2, 7, 11, 13, 17, 19, 23;
2, 3, 5, 11, 13, 17, 19, 23, 29;


PROG

(PARI) isok(k, n) = {if (isprime(2*nk), pf = factor(k)[, 1]; for (j=1, #pf, if (isprime(2*npf[j]), return (1)); ); ); }
row(n) = {my(v = []); for (k=1, 2*n, if (isok(k, n), v = concat(v, 2*nk))); vecsort(v); } \\ Michel Marcus, Mar 02 2019


CROSSREFS



KEYWORD

nonn,easy,tabf


AUTHOR



STATUS

approved



