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A369670
Integers k such that k, k + 1 and 2 k + 1 all have the same number of prime factors, counted with multiplicity.
1
2, 25, 34, 38, 57, 93, 118, 133, 145, 171, 177, 201, 205, 213, 218, 298, 332, 334, 361, 381, 387, 394, 446, 501, 507, 604, 633, 694, 698, 710, 805, 842, 865, 878, 898, 902, 921, 1004, 1075, 1084, 1105, 1114, 1130, 1141, 1172, 1182, 1226, 1285, 1293, 1358, 1412, 1445, 1465, 1513, 1557, 1587, 1592
OFFSET
1,1
LINKS
EXAMPLE
a(3) = 34 is a term because 34 = 2 * 17, 34 + 1 = 35 = 5 * 7 and 2 * 34 + 1 = 69 = 3 * 23 all have 2 prime factors.
MAPLE
filter:= proc(n) local t; uses numtheory; t:= bigomega(n); t = bigomega(n+1) and t = bigomega(2*n+1) end proc:
select(filter, [$1..10000]);
MATHEMATICA
s = {}; Do[If[PrimeOmega[k] == PrimeOmega[k + 1] == PrimeOmega[2 k + 1], AppendTo[s, k]], {k, 1000}]; s
CROSSREFS
Intersection of A045920 and A117360. Contains A188059.
Cf. A001222.
Sequence in context: A264118 A054292 A248546 * A038834 A041071 A153478
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Jan 28 2024
STATUS
approved