A296811 Take a squarefree semiprime and take the difference of its prime factors. If it is a squarefree semiprime repeat the process. Sequence lists the squarefree semiprimes that generate other squarefree semiprimes only in the first k steps of this process. Case k = 4.

687, 1186, 1631, 1906, 1994, 2391, 3107, 3687, 3755, 4786, 5991, 6155, 6218, 7715, 7967, 8306, 8327, 8351, 9298, 9731, 9995, 11567, 12178, 12938, 13391, 13607, 13787, 13863, 14367, 15434, 15506, 15578, 16595, 16658, 16706, 17039, 17687, 18663, 19466, 19631, 21687

Offset

1,1

Comments

For any pair of distinct prime numbers p and q, if p * q belongs to this sequence, then abs(p - q) belongs to A296810. - Rémy Sigrist, Jan 07 2018

Links

Table of n, a(n) for n=1..41.

Example

687 = 3*229, 229-3 = 226 = 2*113, 113-2 = 111 = 3*37, 37-3 = 34 = 2*17, 17-2 = 15 = 3*5 but 5-3 = 2 is not a squarefree semiprime.
1186 = 2*593, 593-2 = 591 = 3*197 = 197-3 = 194 = 2*97 = 97-2 = 95 = 5*19, 19-5 = 14 = 2*7 but 7-2 = 5 is not a squarefree semiprime.

Maple

with(numtheory): P:=proc(n, h) local a, j, ok; ok:=1; a:=n; for j from 1 to h do if issqrfree(a) and nops(factorset(a))=2 then a:=ifactors(a)[2]; a:=a[1][1]-a[2][1]; else ok:=0; break; fi; od; if ok=1 then n; fi; end: seq(P(i, 5), i=1..2*10^3);

Crossrefs

Cf. A001358, A296096, A296808, A296810.

Sequence in context: A203459 A101944 A045150 * A252642 A252084 A211162

Adjacent sequences: A296808 A296809 A296810 * A296812 A296813 A296814

Keyword

nonn,easy

Author

Paolo P. Lava, Dec 21 2017

Status

approved