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A133126
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Semiprimes which are equal to product of two successive primes and also to sum of three successive primes.
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1
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15, 143, 11021, 154433, 159197, 194477, 213443, 364807, 412163, 462391, 484391, 685583, 853751, 1032247, 1299479, 1633283, 2039183, 2108303, 2301253, 2985959, 3474487, 3802499, 3904567, 3960091, 4028033, 4536899, 5048993, 5517797
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OFFSET
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1,1
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LINKS
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David A. Corneth, Table of n, a(n) for n = 1..10000 (first 350 terms form Harvey P. Dale)
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EXAMPLE
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15 = 3*5 = 3 + 5 + 7,
143 = 11*13 = 43 + 47 + 53,
11021 = 103*107 = 3671 + 3673 + 3677,
154433 = 389*397 = 51473 + 51479 + 51481,
159197 = 397*401 = 53051 + 53069 + 53077,
194477 = 439*443 = 64811 + 64817 + 64849,
213443 = 461*463 = 71143 + 71147 + 71153.
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MATHEMATICA
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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 *)
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
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PROG
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(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 }
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
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CROSSREFS
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Sequence in context: A173406 A291619 A071700 * A240158 A255944 A243418
Adjacent sequences: A133123 A133124 A133125 * A133127 A133128 A133129
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KEYWORD
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nonn,easy
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AUTHOR
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Zak Seidov, Sep 19 2007
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EXTENSIONS
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More terms from Stefan Steinerberger and R. J. Mathar, Sep 24 2007
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STATUS
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approved
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