Michael De Vlieger, <a href="/A364628/b364628_1.txt">Table of n, a(n) for n = 1..16807</a>

proposed

approved

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proposed

allocated For p = 7 and n > 0, write n = p^m + k, m >= 0, with maximal p^m <= n, with 0 <= k < p^(m+1) - p^m, then for n such that k=0, a(n)=n, and for Michael De Vliegern such that k > 0, a(n) is the smallest q*a(k), prime q != p, that is not already a term.

1, 2, 4, 8, 16, 32, 7, 3, 6, 12, 24, 48, 64, 14, 9, 18, 36, 72, 96, 128, 28, 27, 54, 108, 144, 192, 256, 56, 81, 162, 216, 288, 384, 512, 112, 243, 324, 432, 576, 768, 1024, 224, 486, 648, 864, 1152, 1536, 2048, 49, 5, 10, 20, 40, 80, 160, 21, 15, 30, 60, 120

1,2

This is sequence D(p), p = 7, where the Doudna sequence A005940 is D(2).

Michael De Vlieger, <a href="/A364628/b364628_1.txt">Table of n, a(n) for n = 1..16807</a>

<a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

p = 7; nn = 343; c[_] = False;

Do[Set[{m, k}, {1, n - p^Floor[Log[p, n]]}];

If[k == 0,

Set[{a[n], c[n]}, {n, True}],

While[Set[t, Prime[m] a[k]]; Or[m == i, c[t]], m++];

Set[{a[n], c[t]}, {t, True}]], {n, nn}];

Array[a, nn]

Cf. A005940 (D(2)), A356867 (D(3)), A364611 (D(5)).

allocated

nonn

Michael De Vlieger, Sep 16 2023

approved

editing

allocated for Michael De Vlieger

recycled

allocated

reviewed

approved

proposed

reviewed

editing

proposed

a(n)=3*n^3-n+1

3, 23, 79, 189, 371, 643, 1023, 1529, 2179, 2991, 3983, 5173, 6579, 8219, 10111, 12273, 14723, 17479, 20559, 23981, 27763, 31923, 36479, 41449, 46851, 52703, 59023, 65829, 73139, 80971, 89343, 98273, 107779, 117879, 128591, 139933, 151923, 164579, 177919

1,1

a(n) is always congruent to 1,3 or 9 mod 10.

a(n)=3*n^3-n+1

For n=7, a(7)=3*7^3-7+1=1023

Table[3*Power[n, 3] - n + 1, {n, 0, 50}]

(Python)

for n in range(50):

n=n+1

print(str(3*n**3-n+1))

nonn,changed

recycled

Bairav Murugan, Aug 24 2023

proposed

editing