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%I #21 Apr 24 2023 12:10:35
%S 15,143,11021,154433,159197,194477,213443,364807,412163,462391,484391,
%T 685583,853751,1032247,1299479,1633283,2039183,2108303,2301253,
%U 2985959,3474487,3802499,3904567,3960091,4028033,4536899,5048993,5517797
%N Semiprimes which are equal to product of two successive primes and also to sum of three successive primes.
%H David A. Corneth, <a href="/A133126/b133126.txt">Table of n, a(n) for n = 1..10000</a> (first 350 terms from Harvey P. Dale)
%e 15 = 3*5 = 3 + 5 + 7,
%e 143 = 11*13 = 43 + 47 + 53,
%e 11021 = 103*107 = 3671 + 3673 + 3677,
%e 154433 = 389*397 = 51473 + 51479 + 51481,
%e 159197 = 397*401 = 53051 + 53069 + 53077,
%e 194477 = 439*443 = 64811 + 64817 + 64849,
%e 213443 = 461*463 = 71143 + 71147 + 71153.
%t b = {}; For[n = 2, n < 1000, n++, a = Prime[n]*Prime[n + 1]; If[a == Prime[PrimePi[a/3]] + Prime[PrimePi[a/3] + 1] + Prime[PrimePi[a/3] + 2] || a == Prime[PrimePi[a/3] - 1] + Prime[PrimePi[a/3]] + Prime[PrimePi[a/3] + 1], AppendTo[b, a]]]; b (* _Stefan Steinerberger_, Sep 24 2007 *)
%t stspQ[n_]:=Module[{ppi=PrimePi[n/3]},MemberQ[Total/@Partition[ Prime[ Range[ ppi-10,ppi+10]],3,1],n]]; With[{nn=500},Select[ Times@@@ Partition[ Prime[Range[nn]],2,1],stspQ]]//Quiet
%o (PARI) upto(n) = {res = List(); q = 2; forprime(p = 3, sqrtint(n), if(is(p*q), listput(res, p*q); print1(p*q", "); ); q = p; ); res }
%o is(n) = { my(pp = precprime(n \ 3), np = nextprime(pp+1)); r = n - pp - np; if(r > np, return(r == nextprime(np + 1)) ); if(r < pp, return(r == precprime(pp - 1)) ); 0 } \\ _David A. Corneth_, Aug 22 2020
%K nonn,easy
%O 1,1
%A _Zak Seidov_, Sep 19 2007
%E More terms from _Stefan Steinerberger_ and _R. J. Mathar_, Sep 24 2007
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