A133126 Semiprimes which are equal to product of two successive primes and also to sum of three successive primes.

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

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 350 terms from Harvey P. Dale)

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A173406 A291619 A071700 * A240158 A255944 A243418

Adjacent sequences: A133123 A133124 A133125 * A133127 A133128 A133129

Keyword

nonn,easy

Author

Zak Seidov, Sep 19 2007

Extensions

More terms from Stefan Steinerberger and R. J. Mathar, Sep 24 2007

Status

approved