A188651 Products of two primes (i.e., "semiprimes") that are the sum of three consecutive primes.

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

Offset

1,1

Comments

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.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

semiPrimeQ[n_Integer] := Total[FactorInteger[n]][[2]] == 2; Select[Total /@ Partition[Prime[Range[100]], 3, 1], semiPrimeQ] (* T. D. Noe, Apr 20 2011 *)

Crossrefs

Sequence in context: A259629 A212794 A048061 * A330203 A272307 A092192

Adjacent sequences: A188648 A188649 A188650 * A188652 A188653 A188654

Keyword

nonn

Author

Zak Seidov, Apr 16 2011

Status

approved