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A188651
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Products of two primes (i.e., "semiprimes") that are the sum of three consecutive primes.
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2
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10, 15, 49, 121, 143, 159, 187, 235, 287, 301, 319, 329, 371, 395, 407, 471, 519, 533, 551, 565, 581, 589, 633, 679, 689, 713, 731, 749, 771, 789, 803, 817, 841, 961, 985, 1079, 1099, 1119, 1135, 1169, 1207, 1271, 1285, 1315, 1349, 1391, 1457, 1477, 1585
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OFFSET
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1,1
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COMMENTS
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Or, semiprimes in A034961 (Sums of three consecutive primes).
Subsequence of square semiprimes: {49, 121, 841, 961, 1849, 22801, 24649, 36481, 69169, ...} = {7, 11, 29, 31, 43, 151, 157, 191, 263, ...}^2 that is also a subsequence of A080665 (Squares in A034961). Cf. also A034962 (Primes A034961).
Somewhat surprisingly, the sum of two consecutive primes is never a semiprime. This follows from that fact that if p+q = 2r for primes p,q,r, then r must between p and q. So if p and q are consecutive, then r does not exist.
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..1000
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EXAMPLE
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a(1) = 10 = 2*5 = A034961(1) = prime(1) + prime(2) + prime(3) = 2 + 3 + 5,
a(2) = 15 = 3*5 = A034961(2) = prime(2) + prime(3) + prime(4) = 3 + 5 + 7,
a(3) = 49 = 7*7 = A080665(1) = A034961(6) = prime(6) + prime(7) + prime(8) = 13 + 17 + 19.
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MATHEMATICA
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semiPrimeQ[n_Integer] := Total[FactorInteger[n]][[2]] == 2; Select[Total /@ Partition[Prime[Range[100]], 3, 1], semiPrimeQ] (* T. D. Noe, Apr 20 2011 *)
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CROSSREFS
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Sequence in context: A259629 A212794 A048061 * A330203 A272307 A092192
Adjacent sequences: A188648 A188649 A188650 * A188652 A188653 A188654
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov, Apr 16 2011
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STATUS
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approved
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