1,1

Semiprimes in arithmetic progression. All terms are odd, see also A056809.

Exactly one of the numbers in these arithmetic progressions is of the form 7*p, p prime. - David A. Corneth, Sep 11 2025

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 500 terms from Robert Israel)

David A. Corneth, PARI programs

R:= NULL: count:= 0: state:= 0:

for n from 1 by 2 while count < 40 do

if numtheory:-bigomega(n) = 2 then state:= state+1 else state:= 0 fi;

if state >= 7 then R:= R, n-12; count:= count+1 fi

od:

R; # Robert Israel, Sep 11 2025

PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] & /@ FactorInteger[n]]; Select[ Range[ 631200], PrimeFactorExponentsAdded[ # ] == PrimeFactorExponentsAdded[ # + 2] == PrimeFactorExponentsAdded[ # + 4] == PrimeFactorExponentsAdded[ # + 6] == PrimeFactorExponentsAdded[ # + 8] == PrimeFactorExponentsAdded[ # + 10] == PrimeFactorExponentsAdded[ # + 12] == 2 &] (* Robert G. Wilson v, Feb 24 2004 *)

Select[Range[610000], Union[PrimeOmega[#+Range[0, 12, 2]]]=={2}&] (* Harvey P. Dale, Oct 14 2018 *)

(PARI) \\ See Corneth link

Cf. A056809, A070552, A092125, A092126, A092127, A092128.

Sequence in context: A268578 A268862 A277786 * A251871 A206132 A187305

Adjacent sequences: A092126 A092127 A092128 * A092130 A092131 A092132

Zak Seidov, Feb 22 2004

More terms from Don Reble, Feb 23 2004

More terms from Robert G. Wilson v, Feb 24 2004

approved