A217030 Semiprimes p such that next semiprime after p is p + 10.

237, 427, 1027, 1101, 1661, 2723, 2747, 3173, 3295, 3669, 3849, 3873, 3963, 4087, 4227, 4237, 4667, 4717, 4897, 5007, 5017, 5277, 5837, 6145, 6249, 6445, 6697, 6757, 6787, 6943, 7483, 8373, 9169, 9183, 9543, 9673, 9691, 9903, 10063, 10135, 10239, 10523, 10981

Offset

1,1

Comments

First pair of successive semiprimes with gap 10 is {237 = 3*79, 247 = 13*19}. First triple of successive semiprimes with gaps 10 is {4227 = 3*1409, 4237 = 19*223, 4247 = 31*137}. First quadruple of successive semiprimes with gaps 10 is {63643 = 31*2053, 63653 = 53*1201, 63663 = 3*21221, 63673 = 41*1553}. First 5 successive semiprimes with gaps 10 are {1381951 = 103*13417, 1381961 = 7*197423, 1381971 = 3*460657, 1381981 = 17*81293, 1381991 = 13*106307}. First 6 successive semiprimes with gaps 10 are {16476607 = 7*2353801, 16476617 = 557*29581, 16476627 = 3*5492209, 16476637 = 3677*4481, 16476647 = 11*1497877, 16476657 = 3*5492219}.

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Mathematica

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; t = Select[Range[11000], SemiPrimeQ[#] &]; t2 = Differences[t]; t[[Flatten[Position[t2, 10]]]] (* T. D. Noe, Sep 24 2012 *)
Select[Partition[Select[Range[11000], PrimeOmega[#]==2&], 2, 1], #[[2]]-#[[1]]==10&][[;; , 1]] (* Harvey P. Dale, Jan 29 2024 *)

Prog

(Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [n: n in [4..13000] | IsSemiprime(n) and IsSemiprime(n+10) and forall{n+i: i in [1..9] | not IsSemiprime(n+i)}]; // Bruno Berselli, Oct 01 2012

Crossrefs

Cf. A001358.

Sequence in context: A265372 A252718 A036270 * A048454 A255618 A237592

Adjacent sequences: A217027 A217028 A217029 * A217031 A217032 A217033

Keyword

nonn

Author

Zak Seidov, Sep 24 2012

Status

approved