A296813 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 = 6.

14367, 16706, 18663, 28738, 33551, 49983, 58407, 62387, 68519, 77195, 82743, 97355, 137042, 137915, 143223, 149327, 155114, 181163, 183818, 214247, 238715, 262667, 331211, 332363, 370343, 373763, 384767, 405434, 406743, 448247, 503567, 503834, 522983, 576951, 634115

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Example

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.
16706 = 2*8353, 8353-2 = 8351 = 7*1193, 1193-7 = 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, 7), i=1..2*10^3);

Crossrefs

Sequence in context: A249207 A049442 A228468 * A234678 A237788 A106725

Adjacent sequences: A296810 A296811 A296812 * A296814 A296815 A296816

Keyword

nonn,easy

Author

Paolo P. Lava, Dec 21 2017

Status

approved