A121387 Semiprimes p*q with p and q primes of the form 4k+1 (A002144).

25, 65, 85, 145, 169, 185, 205, 221, 265, 289, 305, 365, 377, 445, 481, 485, 493, 505, 533, 545, 565, 629, 685, 689, 697, 745, 785, 793, 841, 865, 901, 905, 949, 965, 985, 1037, 1073, 1145, 1157, 1165, 1189, 1205, 1241, 1261, 1285, 1313, 1345, 1369, 1385, 1405, 1417

Offset

1,1

Comments

p and q can be the same. [Harvey P. Dale, Jan 15 2012]

The terms are semiprimes of the form 4k + 1, and comprise only a portion of all such semiprimes, see A108181. - Richard R. Forberg, Aug 27 2013

Links

François Huppé, Table of n, a(n) for n = 1..10000 (First 1000 terms from T. D. Noe).

Example

65 = 5 * 13. Note that 5 mod 4 = 1 and 13 mod 4 = 1, so 65 is a term.

Mathematica

With[{prs=Select[Prime[Range[150]], Mod[#, 4]==1&]}, Take[Union[Times @@@ Tuples[prs, 2]], 60]] (* Harvey P. Dale, Jan 15 2012 *)

Prog

(Python)
from math import isqrt
from sympy import primerange
from oeis_sequences.OEISsequences import bisection
def A121387(n):
    def g(x): return sum(1 for p in primerange(5, x+1) if p&3==1)
    def f(x): return int(n+x+((t:=g(s:=isqrt(x)))*(t-1)>>1)-sum(g(x//p) for p in primerange(5, s+1) if p&3==1))
    return bisection(f, n, n) # Chai Wah Wu, Dec 20 2025

Crossrefs

Cf. A001358, A002144.

Fifth row of A121388.

Union of A080109 and A131574.

Cf. A107978, A080774, A108181.

Sequence in context: A120961 A285579 A050993 * A039376 A043199 A043979

Adjacent sequences: A121384 A121385 A121386 * A121388 A121389 A121390

Keyword

easy,nonn

Author

Alford Arnold, Jul 26 2006, corrected Jun 24 2007

Extensions

Better definition from T. D. Noe, Sep 25 2007

Status

approved