A360377 - OEIS

A360377

a(n) = number of the row of the Wythoff array (A035513) that includes prime(n).

1, 1, 1, 2, 2, 1, 7, 8, 6, 2, 8, 6, 10, 17, 2, 21, 23, 24, 26, 11, 7, 12, 20, 1, 6, 39, 40, 10, 26, 17, 49, 8, 53, 21, 14, 36, 6, 63, 40, 10, 69, 27, 7, 46, 76, 2, 81, 33, 54, 88, 1, 92, 14, 23, 38, 64, 66, 42, 27, 74, 18, 80, 84, 53, 54, 90, 94, 59, 60, 24

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OFFSET

1,4

COMMENTS

Conjecture: every primitive row number, as defined in A332938, occurs infinitely many times in this sequence.

LINKS

Table of n, a(n) for n=1..70.

FORMULA

Every prime p has a unique representation p = p(m,k) = F(k+1)*[m*tau] + (m-1)*F(k), where F(h) = A000045(h) = h-th Fibonacci number, [ ] = floor, and tau = (1+sqrt(5))/2 = golden ratio, as in A001622. Here, a(n) is the number m such that prime(n) = p(m,k) for some k.

EXAMPLE

The 10th prime is 29, which occurs in row 7, so a(10) = 2.

MATHEMATICA

W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];

t = Table[W[n, k], {n, 100}, {k, 1, 20}];

a[n_] := Select[Range[100], MemberQ[t[[#]], Prime[n]] &]

Flatten[Table[a[n], {n, 1, 100}]]

CROSSREFS

Cf. A000040, A035513, A332938, A360378, A360379, A360380.

Sequence in context: A136502 A144502 A246945 * A100632 A225925 A357553

Adjacent sequences: A360374 A360375 A360376 * A360378 A360379 A360380

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 04 2023

STATUS

approved