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A374023
Numbers m such that m .. m+11 all have the same number of prime factors, counted with multiplicity.
1
3195380868, 5208143601, 5208143602, 5327400945, 5604994082, 5604994083, 6940533603, 6940533604, 7109053186, 7112231268, 19355940562, 22180594465, 24073076004, 24155988484, 29495293764, 30997967601, 41999754228, 42322452483, 42322452484, 45479198003, 46553917683
OFFSET
1,1
COMMENTS
Since a(3) = a(2) + 1, a(6) = a(5) + 1 and a(8) = a(7) + 1, a(2) = 5208143601, a(5) = 5604994082 and a(7) = 6940533603 are the first three m such that m .. m+12 have the same number of prime factors, counted with multiplicity.
For n <= 12, A001222(a(n)) = 4. It must always be at least 4 because at least one of a(n) .. a(n)+11 is divisible by 8.
LINKS
FORMULA
A001222(a(n)) = A001222(a(n)+1) = ... = A001222(a(n)+11).
EXAMPLE
5208143601 is a term because
5208143601 = 3 * 139 * 2153 * 5801
5208143602 = 2 * 47 * 4261 * 13003
5208143603 = 13 * 103 * 419 * 9283
5208143604 = 2^2 * 3 * 434011967
5208143605 = 5 * 7^2 * 21257729
5208143606 = 2 * 37 * 109 * 645691
5208143607 = 3^2 * 647 * 894409
5208143608 = 2^3 * 651017951
5208143609 = 73^2 * 367 * 2663
5208143610 = 2 * 3 * 5 * 173604787
5208143611 = 11 * 29 * 1129 * 14461
5208143612 = 2^2 * 7 * 186005129
all have 4 prime factors, counted with multiplicity.
PROG
(PARI) isok(m) = #Set(apply(bigomega, vector(11, i, m+i-1))) == 1; \\ Michel Marcus, Jul 11 2024
CROSSREFS
Subsequence of A033987.
Cf. A001222.
Numbers m through m+k have the same value of A001222: A045920 (k=1), A045939 (k=2), A045940 (k=3), A045941 (k=4), A045942 (k=5), A123103 (k=6), A123201 (k=7), A358017 (k=8), A358018 (k=9), A358019 (k=10).
Sequence in context: A217051 A198863 A199630 * A198298 A074773 A340133
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Jun 25 2024
EXTENSIONS
Missing term inserted by, and more terms from Martin Ehrenstein, Jul 11 2024
STATUS
approved