A296810 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 = 3.

226, 327, 543, 591, 623, 687, 746, 791, 794, 951, 995, 1186, 1226, 1538, 1623, 1631, 1906, 1919, 1994, 2018, 2031, 2391, 2463, 2483, 3107, 3314, 3503, 3587, 3687, 3743, 3755, 4115, 4151, 4247, 4618, 4647, 4786, 5127, 5627, 5991, 6087, 6155, 6218, 6407, 6423, 6467

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

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.
327 = 3*109, 109-3 = 106 = 2*53, 53-2 = 51 = 3*17, 17-3 = 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, 4), i=1..2*10^3);

Crossrefs

Cf. A001358, A296096, A296808.

Sequence in context: A296898 A265499 A126897 * A067265 A218040 A158229

Adjacent sequences: A296807 A296808 A296809 * A296811 A296812 A296813

Keyword

nonn,easy

Author

Paolo P. Lava, Dec 21 2017

Status

approved