Krishna Kumar Arumugam has authored 3 sequences.
A353957
a(n) = (85*4^n - 1)/3.
Original entry on oeis.org
113, 453, 1813, 7253, 29013, 116053, 464213, 1856853, 7427413, 29709653, 118838613, 475354453, 1901417813, 7605671253, 30422685013, 121690740053, 486762960213, 1947051840853, 7788207363413, 31152829453653, 124611317814613, 498445271258453, 1993781085033813
Offset: 1
When n=5, a(5) = 29013 and when iterated using the Collatz function will have the following trajectory: 87040,43520,21760,10880,5440,2720,1360,680,340,170,85,256,128,64,32,16,8,4,2,1
A354227
Odd numbers whose Collatz trajectory contains exactly 12 odd numbers.
Original entry on oeis.org
39, 79, 153, 157, 305, 307, 315, 317, 611, 613, 629, 631, 647, 683, 687, 1221, 1229, 1241, 1257, 1261, 1265, 1269, 1295, 1353, 1367, 1369, 1375, 1505, 2445, 2453, 2481, 2483, 2489, 2507, 2515, 2517, 2521, 2525, 2531, 2545, 2589, 2593, 2633, 2705, 2707, 2733
Offset: 1
305 is a term since its Collatz trajectory is 305, 916, 458, 229, 688, 344, 172, 86, 43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
A354170
Odd numbers whose Collatz trajectory includes 11 odd numbers.
Original entry on oeis.org
57, 59, 115, 119, 229, 237, 461, 465, 473, 477, 507, 513, 917, 931, 943, 945, 947, 949, 971, 987, 1015, 1025, 1027, 1031, 1129, 1131, 1845, 1857, 1861, 1867, 1881, 1887, 1891, 1893, 1905, 1909, 1943, 1945, 1953, 1975, 2029, 2051, 2053, 2055, 2059, 2063, 2073
Offset: 1
119 is a term since its Collatz trajectory is 119, 358, 179, 538, 269, 808, 404, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 29, 10, 5, 16, 8, 4, 2, 1, which has 11 odd numbers.
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b:= proc(n) option remember; irem(n, 2, 'r')+
`if`(n=1, 0, b(`if`(n::odd, 3*n+1, r)))
end:
q:= n-> is(n::odd and b(n)=11):
select(q, [$1..5000])[]; # Alois P. Heinz, May 18 2022
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q[n_] := Count[NestWhileList[If[OddQ[#], 3 # + 1, #/2] &, n, # > 1 &], ?OddQ] == 11; Select[2*Range[1000] - 1, q] (* _Amiram Eldar, May 18 2022 *)
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