A296809 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 = 2.

82, 106, 111, 178, 194, 226, 287, 314, 327, 371, 395, 411, 538, 543, 586, 591, 611, 623, 674, 687, 695, 746, 767, 791, 794, 815, 818, 898, 951, 995, 1007, 1043, 1186, 1226, 1347, 1418, 1466, 1514, 1538, 1546, 1623, 1631, 1655, 1703, 1706, 1851, 1883, 1906, 1919

Offset

1,1

Links

Table of n, a(n) for n=1..49.

Example

82 = 2*41, 41-2 = 39 = 3*13, 13-3 = 10 = 2*5 but 5-2 = 3 is not a squarefree semiprime.
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 doif 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, 3), i=1..2*10^3);

Crossrefs

Cf. A001358, A296096, A296808.

Sequence in context: A316573 A294308 A025361 * A223085 A260761 A037159

Adjacent sequences: A296806 A296807 A296808 * A296810 A296811 A296812

Keyword

nonn,easy

Author

Paolo P. Lava, Dec 21 2017

Status

approved