A296812 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 = 5.

4786, 5991, 6218, 8351, 9995, 13391, 14367, 15434, 16658, 16706, 18663, 19466, 27578, 28738, 33551, 34082, 34187, 37727, 38823, 41555, 45251, 46391, 46743, 47738, 49983, 52847, 57458, 58407, 62387, 67191, 68519, 69567, 75111, 77195, 77555, 77915, 82743, 83807, 87807

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 A296811. - Rémy Sigrist, Jan 07 2018

Links

Table of n, a(n) for n=1..39.

Example

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.
5991 = 3*1997, 1997-3 = 1994 = 2*997, 997-2 = 995 = 5*199, 199-5 = 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, 6), i=1..2*10^3);

Crossrefs

Cf. A001358, A296096, A296808, A296811.

Sequence in context: A237095 A138087 A354086 * A251775 A096517 A221005

Adjacent sequences: A296809 A296810 A296811 * A296813 A296814 A296815

Keyword

nonn,easy

Author

Paolo P. Lava, Dec 21 2017

Status

approved