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URL: https://oeis.org/A076804

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A076804
a(n) = least positive integer k satisfying Omega(k) = Omega(k+1)+Omega(k+2)....+Omega(k+n), where Omega = A001222 = number of prime factors, counting multiplicity.
0
2, 12, 64, 4608, 2304, 193536, 1572864, 566231040, 1879048192, 167503724544, 850403524608, 79164837199872, 3595815339687936, 69084514596421632, 1801439850948198400
OFFSET
1,1
COMMENTS
a(16) > 2^63. - Donovan Johnson, Sep 27 2008
a(16) <= 1154362656487605534720. - Giovanni Resta, Apr 01 2020
EXAMPLE
k=2 is the least solution of Omega(k) = Omega(k+1), so a(1) = 2.
k=12 is the least solution of Omega(k) = Omega(k+1)+Omega(k+2), so a(2) = 12.
k=64 is the least solution of Omega(k) = Omega(k+1)+Omega(k+2)+Omega(k+3), so a(3) = 64.
k=4608 is the least solution of Omega(k) = Omega(k+1)+Omega(k+2)+Omega(k+3)+Omega(k+4), so a(4) = 4608.
MATHEMATICA
(* This is only a recomputation of the existing sequence. *)
selQ[n_, k_] := PrimeOmega[k] == Sum[PrimeOmega[k + j], {j, 1, n}];
T = Table[2^k2 3^k3 5^k5 7^k7 11^k11 13^k13 17^k17 19^k19, {k2, 1, 56}, {k3, 0, 4}, {k5, 0, 2}, {k7, 0, 1}, {k11, 0, 1}, {k13, 0, 1}, {k17, 0, 1}, {k19, 0, 1}] // Flatten // Sort;
a[n_] := SelectFirst[T, selQ[n, #]&];
Reap[Do[Print[n, " ", an = a[n]]; Sow[an], {n, 1, 15}]][[2, 1]] (* Jean-François Alcover, Mar 27 2020 *)
PROG
(PARI) A078114(n, ok=0)={ local( MIN=n+sum(i=2, n, bigomega(i)), t, k ); until( !t & k==ok+n, while( MIN>t=bigomega(ok++), ); k=ok; while( 0 < t-=bigomega(k++), )); ok} \\ M. F. Hasler, Jun 17 2007
CROSSREFS
Sequence in context: A126737 A345697 A097632 * A190153 A372369 A369111
KEYWORD
hard,more,nonn
AUTHOR
Shyam Sunder Gupta, Nov 17 2002
EXTENSIONS
Corrected & edited by M. F. Hasler, Jun 17 2007
a(9)-a(15) from Donovan Johnson, Sep 27 2008
STATUS
approved