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A370205
Numbers j whose symmetric representation of sigma(j) consists of the single unimodal width pattern 121.
5
6, 12, 20, 24, 28, 40, 48, 56, 80, 88, 96, 104, 112, 160, 176, 192, 208, 224, 272, 304, 320, 352, 368, 384, 416, 448, 464, 496, 544, 608, 640, 704, 736, 768, 832, 896, 928, 992, 1088, 1184, 1216, 1280, 1312, 1376, 1408, 1472, 1504, 1536, 1664, 1696, 1792, 1856, 1888, 1952, 1984
OFFSET
1,1
COMMENTS
Every term has 2 odd divisors and has the form 2^k * p, k > 0, p prime and 2 < p < 2^(k+1), and therefore is a subsequence of A082662. The two 1's in row a(n) of the triangle of A237048 occur in positions 1 and p up to the diagonal since p <= floor( (sqrt(8*a(n) + 1) - 1)/2 ) < 2^(k+1) which represents the unimodal width pattern 121 in SRS(a(n)).
Numbers in this sequence divisible by 5 have the form 2^(k+2) * 5, k >= 0, the least being a(3) = 20.
MATHEMATICA
(* function based on conditions for the odd divisors - fast computation *)
a370205Q[n_] := Module[{p=NestWhile[#/2&, n, EvenQ[#]&]}, PrimeQ[p]&&p^2<2n)]
a370205[m_, n_] := Select[Range[m, n], a370205Q]
a370205[1, 1984]
(* widthPattern[ ] and support functions are defined in A341969 - slow computation *)
a370205[m_, n_] := Select[Range[m, n], widthPattern[#]=={1, 2, 1}&]
a370205[1, 1984]
KEYWORD
nonn
AUTHOR
Hartmut F. W. Hoft, Feb 11 2024
STATUS
approved