Sam Chapman - cp's OEIS frontend

User: Sam Chapman

Sam Chapman has authored 3 sequences.

A381501 Positive integers that do not appear in A381466.

1, 12, 14, 17, 26, 28, 30, 33, 35, 38, 46, 49, 50, 56, 68, 74, 85, 86, 92, 93, 96, 98, 104, 105, 106, 110, 122, 124, 132, 134, 140, 156, 164, 166, 170, 182, 188, 190, 194, 195, 200, 202, 214, 218, 226, 236, 242, 248, 250, 254, 260, 284, 285, 290, 302, 304, 305, 308, 310, 314, 320, 326, 336, 338, 344, 346, 350, 362, 368, 374, 375

Offset: 1

Sam Chapman, Feb 25 2025

nonn

The sequence appears to grow linearly and is approximately 5.42*n.

A381495(k) = 0 if and only if k appears in this sequence.

Sam Chapman, Table of n, a(n) for n = 1..366

Cf. A381466, A381495.

A381495 a(n) is the number of times n appears in A381466.

Original entry on oeis.org

0, 2, 2, 1, 3, 1, 5, 2, 3, 2, 2, 0, 2, 0, 2, 1, 0, 1, 4, 2, 3, 2, 3, 1, 6, 0, 1, 0, 4, 0, 5, 2, 0, 1, 0, 1, 6, 0, 4, 1, 3, 2, 3, 1, 1, 0, 2, 1, 0, 0, 2, 2, 4, 1, 3, 0, 4, 1, 4, 1, 4, 1, 1, 3, 1, 4, 2, 0, 1, 1, 2, 1, 3, 0, 2, 3, 3, 1, 2, 3, 1, 1, 2, 1, 0, 0, 2, 1, 1, 2, 4, 0, 0, 2, 1, 0, 3, 0, 2, 1, 2, 1, 2, 0, 0, 0, 3, 2, 3, 0, 3, 1, 3, 1, 1, 2, 4, 1, 3, 1, 3, 0, 1, 0, 2, 1, 4, 1, 1, 1

Offset: 1

Sam Chapman, Feb 25 2025

nonn

The sequence is well defined, as we have proven that A381466(n) > sqrt(n/6) for all n, and thus each number can only appear a finite amount of times in A381466.

It appears that this sequence has an average value of approximately 1.755

Sam Chapman, Table of n, a(n) for n = 1..2000

Cf. A381466, A381501 (indices of 0's).

A381466 a(0) = 4; for n > 0, a(n) = a(n-1) + n if G = 1 or a(n) = n/G if G > 1, where G = gcd(a(n-1), n).

Original entry on oeis.org

4, 5, 7, 10, 2, 7, 13, 20, 2, 11, 21, 32, 3, 16, 7, 22, 8, 25, 43, 62, 10, 31, 53, 76, 6, 31, 57, 9, 37, 66, 5, 36, 8, 41, 75, 7, 43, 80, 19, 58, 20, 61, 103, 146, 22, 67, 113, 160, 3, 52, 25, 76, 13, 66, 9, 64, 7, 64, 29, 88, 15, 76, 31, 94, 32, 97, 163, 230, 34, 103, 173, 244

Offset: 0

Sam Chapman, Feb 24 2025

nonn

If a(n) < n for some n, then a(n+1) > n+1.
If a(n) > n, a(n+1) > n+1, and a(n+2) > n+2 for some n, then a(n+3) < n+3.
1 < a(n) for all n.
sqrt(n/6) < a(n) <= 7n/2 - 9/2 for all n.
a(p)>p for all primes p.
If one were to use the same rule to generate this sequence with any other initial value that is congruent to 4 or 8 (mod 12), that sequence would agree with this one for all n>3.
If one were to use the same rule to generate this sequence with an initial term that is not congruent to 4 or 8 (mod 12), then it would output the number 1 before the 5th term. When a sequence follows a(n)’s rules and outputs the number 1 at some index k, one gets the following quasi-periodic behavior: 1, k+2, 1, k+4, 1, k+6, etc., and are as such “boring” sequences.

			a(12) = 3 and gcd(3, 13) = 1, so a(13) = 3 + 13 = 16.  gcd(16, 14) = 2, so a(14) = 14/2 = 7.

Sam Chapman, Table of n, a(n) for n = 0..10000

Similar to A133058, A091508.

s={4};Do[G=GCD[s[[-1]],n];AppendTo[s,If[G==1,s[[-1]]+n,n/G]],{n,71}];s (* James C. McMahon, Mar 02 2025 *)

lista(nn) = my(v = vector(nn)); v[1] = 4; for (n=2, nn, my(g=gcd(v[n-1], n-1)); if (g==1, v[n] = v[n-1] + n-1, v[n] = (n-1)/g);); v; \\ Michel Marcus, Feb 26 2025

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User: Sam Chapman

A381501 Positive integers that do not appear in A381466.

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A381495 a(n) is the number of times n appears in A381466.

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A381466 a(0) = 4; for n > 0, a(n) = a(n-1) + n if G = 1 or a(n) = n/G if G > 1, where G = gcd(a(n-1), n).

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