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 A281838 Semiprimes that are the sum of 2, 3, 4, and 5 consecutive semiprimes. 1

%I #34 Jun 26 2017 04:16:21

%S 2705,88041,218729,348242,654802,659083,754462,1259383,1928911,

%T 2126545,2748374,3226321,3369122,3893087,3913922,4063289,4252843,

%U 4605151,4631323,6024338,6482539,7090654,8079467,8759071,9669602,9976679,10209674,10603319,10943599,13448837,13550506

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

%C a(36)=16626281 and a(68)=55710962 are also the sum of 6 consecutive semiprimes. - _Zak Seidov_, Jun 20 2017

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

%H Zak Seidov, <a href="/A281838/b281838.txt">Table of n, a(n) for n = 1..2200</a> (a(8)-a(111) from Robert G. Wilson v)

%e a(1) =

%e A001358(762) = 2705 =

%e A001358(398) + A001358(399) = 1351 + 1354 =

%e A001358(270) + ... + A001358(272) = 899 + 901 + 905 =

%e A001358(201) + ... + A001358(204) = 671 + 674 + 679 + 681 =

%e A001358(167) + ... + A001358(171) = 537 + 538 + 542 + 543 + 545.

%t sp = Select[Range@ 10^7, PrimeOmega@# == 2 &];

%t l2 = Union[ Plus @@@ Partition[ Select[ sp, # < 10^7/2 &], 2, 1]];

%t l3 = Union[ Plus @@@ Partition[ Select[ sp, # < 10^7/3 &], 3, 1]];

%t l4 = Union[ Plus @@@ Partition[ Select[ sp, # < 10^7/4 &], 4, 1]];

%t l5 = Union[ Plus @@@ Partition[ Select[ sp, # < 10^7/5 &], 5, 1]];

%t Intersection[sp, l2, l3, l4, l5] (* _Robert G. Wilson v_, Jan 31 2017 *)

%Y Cf. A001358.

%K nonn

%O 1,1

%A _Zak Seidov_, Jan 31 2017

%E a(8) onward from _Robert G. Wilson v_, Jan 31 2017

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Last modified June 8 03:07 EDT 2023. Contains 363157 sequences. (Running on oeis4.)