A281838 Semiprimes that are the sum of 2, 3, 4, and 5 consecutive semiprimes.

2705, 88041, 218729, 348242, 654802, 659083, 754462, 1259383, 1928911, 2126545, 2748374, 3226321, 3369122, 3893087, 3913922, 4063289, 4252843, 4605151, 4631323, 6024338, 6482539, 7090654, 8079467, 8759071, 9669602, 9976679, 10209674, 10603319, 10943599, 13448837, 13550506

Offset

1,1

Comments

a(36)=16626281 and a(68)=55710962 are also the sum of 6 consecutive semiprimes. - Zak Seidov, Jun 20 2017

Terms a(926)=1241801401 and a(1982)=3254552229 are also the sum of 6 and 7 consecutive semiprimes. - Zak Seidov, Jun 23 2017

Links

Zak Seidov, Table of n, a(n) for n = 1..2200 (a(8)-a(111) from Robert G. Wilson v)

Example

a(1) =
A001358(762) = 2705 =
A001358(398) + A001358(399) = 1351 + 1354 =
A001358(270) + ... + A001358(272) = 899 + 901 + 905 =
A001358(201) + ... + A001358(204) = 671 + 674 + 679 + 681 =
A001358(167) + ... + A001358(171) = 537 + 538 + 542 + 543 + 545.

Mathematica

sp = Select[Range@ 10^7, PrimeOmega@# == 2 &];
  l2 = Union[ Plus @@@ Partition[ Select[ sp, # < 10^7/2 &], 2, 1]];
  l3 = Union[ Plus @@@ Partition[ Select[ sp, # < 10^7/3 &], 3, 1]];
  l4 = Union[ Plus @@@ Partition[ Select[ sp, # < 10^7/4 &], 4, 1]];
  l5 = Union[ Plus @@@ Partition[ Select[ sp, # < 10^7/5 &], 5, 1]];
Intersection[sp, l2, l3, l4, l5] (* Robert G. Wilson v, Jan 31 2017 *)

Crossrefs

Cf. A001358.

Sequence in context: A250615 A193172 A367668 * A205605 A205436 A031550

Adjacent sequences: A281835 A281836 A281837 * A281839 A281840 A281841

Keyword

nonn

Author

Zak Seidov, Jan 31 2017

Extensions

a(8) onward from Robert G. Wilson v, Jan 31 2017

Status

approved