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A108278 Numbers k such that k^2-1 and k^2+1 are semiprimes. 6
12, 30, 42, 60, 102, 108, 198, 312, 462, 522, 600, 810, 828, 1020, 1050, 1062, 1278, 1452, 1488, 1872, 1950, 2028, 2130, 2142, 2340, 2790, 2802, 2970, 3000, 3120, 3252, 3300, 3330, 3672, 3930, 4020, 4092, 4230, 4548, 4800, 5280, 5640, 5652, 5658, 6198 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A069062. - Michel Marcus, Jan 22 2016

Subsequence of A014574. - Robert Israel, Jan 24 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1)=12 because 12^2-1=143=11*13 and 12^2+1=145=5*29 are both semiprimes.

MAPLE

filter:= n -> isprime(n+1) and isprime(n-1) and numtheory:-bigomega(n^2+1)=2:

select(filter, [seq(i, i=2..1000, 2)]); # Robert Israel, Jan 24 2016

MATHEMATICA

Select[Range[7000], PrimeOmega[#^2 - 1] == PrimeOmega[#^2 + 1]== 2 &] (* Vincenzo Librandi, Jan 22 2016 *)

PROG

(MAGMA) IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [4..7000] | IsSemiprime(n^2+1) and IsSemiprime(n^2-1) ]; // Vincenzo Librandi, Jan 22 2016

(PARI) isok(n) = (bigomega(n^2-1) == 2) && (bigomega(n^2+1) == 2); \\ Michel Marcus, Jan 22 2016

CROSSREFS

Cf. A001358 (semiprimes), A069062 (k^2-1 and k^2+1 have the same number of divisors), A014574 (average of twin prime pairs).

Sequence in context: A325802 A326019 A145470 * A298077 A135502 A256620

Adjacent sequences:  A108275 A108276 A108277 * A108279 A108280 A108281

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, May 30 2005

STATUS

approved

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Last modified October 13 18:14 EDT 2019. Contains 327981 sequences. (Running on oeis4.)