A108278 Numbers k such that k^2-1 and k^2+1 are semiprimes.

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

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: A328411 A333840 A145470 * A364975 A298077 A135502

Adjacent sequences: A108275 A108276 A108277 * A108279 A108280 A108281

Keyword

nonn

Author

Hugo Pfoertner, May 30 2005

Status

approved