

A179502


Numbers k with the property that k^2, k^2+1 and k^2+2 are all semiprimes.


2



11, 29, 79, 271, 379, 461, 521, 631, 739, 881, 929, 1459, 1531, 1709, 2161, 2239, 2341, 2729, 3049, 3491, 3709, 4021, 4349, 4561, 4691, 5021, 5281, 5851, 5879, 6301, 6329, 6829, 7559, 8009, 9151, 10069, 10099, 10151, 10529, 10891, 11719, 11959, 11969, 13799, 14051, 14159
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OFFSET

1,1


COMMENTS

From the first 10^6 primes, 6680 are terms of the sequence.
Also, all numbers k^2+1 are twice prime, and k^2+2 are thrice prime.
The number of terms less than 10^m beginning with m = 1: 0, 3, 11, 35, 160, 759, 4668, 30319, 204439, ..., .
The number of terms less than the (10^m)th prime beginning with m = 1: 2, 7, 33, 165, 941, 6680, 48977, 373627, ..., .


LINKS



MATHEMATICA

fQ[n_] := PrimeQ[(n^2 + 1)/2] && PrimeQ[(n^2 + 2)/3]; Select[ Prime@ Range@ 1667, fQ] (* Robert G. Wilson v, Feb 26 2011 *)


PROG

(PARI){n=10; for(i=1, 10^4, n=nextprime(n+1); n2=n^2; if(2==bigomega(n2+1)&&2==bigomega(n2+2), print1(n, ", ")))}


CROSSREFS

n^2 are squares in A070552, which is a subsequence of A056809 (m and m+1 are semiprimes) and A001358 (semiprimes).
The sequence is a subsequence of A048161.


KEYWORD

nonn


AUTHOR



STATUS

approved



