A296815 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 = 8.

373763, 2276543, 4710863, 5840138, 6108239, 6443183, 6458303, 6983939, 7136306, 7861439, 7997915, 8212934, 9861599, 11261531, 11834786, 11921123, 12204659, 13520063, 13851443, 15236327, 15827978, 17312258, 17632739, 18661922, 19432739, 19523195, 19793603, 20301986, 20335439, 20441459

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Example

373763 = 13*28751, 28751-13 = 28738 = 2*14369, 14369-2 = 14367 = 3*4789, 4789-3 = 4786 = 2*2393, 2393-2 = 2391 = 3*797, 797-3 = 794 = 2*397, 397-2 = 395 = 5*79 = 79-5 = 74 = 2*37, 37-2 = 35 = 5*7 but 7-5 = 2 is not a squarefree semiprime.
2276543 = 79*28817, 28817-79 = 28738 = 2*14369, 14369-2 = 14367 = 3*4789, 4789-3 = 4786 = 2*2393, 2393-2 = 2391 = 3*797, 797-3 = 794 = 2*397, 397-2 = 395 = 5*79 = 79-5 = 74 = 2*37, 37-2 = 35 = 5*7 but 7-5 = 2 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, 9), i=1..10^8);

Crossrefs

Cf. A001358, A296096, A296808.

Sequence in context: A250456 A043661 A206666 * A147770 A218398 A089444

Adjacent sequences: A296812 A296813 A296814 * A296816 A296817 A296818

Keyword

nonn,easy

Author

Paolo P. Lava, Dec 21 2017

Status

approved