A108544 -id:A108544 - cp's OEIS frontend

A108542 Greater prime factor of n-th golden semiprime.

3, 5, 11, 17, 31, 37, 47, 59, 67, 109, 127, 157, 163, 167, 173, 211, 241, 263, 271, 293, 313, 367, 389, 439, 449, 457, 503, 571, 593, 613, 619, 643, 661, 677, 701, 727, 739, 787, 823, 911, 983, 991, 1021, 1069, 1163, 1187, 1231, 1289, 1381, 1429, 1487, 1523

Offset: 1

Reinhard Zumkeller, Jun 09 2005

nonn

abs(phi*A108541(n) - a(n)) < 1, where phi = golden ratio = (1+sqrt(5))/2.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001622, A084127, A108540, A108541, A108543, A108544.

Subsequence of A108539.

f[p_] := Module[{x = GoldenRatio * p}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; q = If[x - p1 < p2 - x, p1, p2]; If[Abs[q - x] < 1, q, 0]]; seq = {}; p=1; Do[p = NextPrime[p]; q = f[p]; If[q > 0, AppendTo[seq, q]], {200}]; seq (* Amiram Eldar, Nov 28 2019 *)

a(n) = A108540(n)/A108541(n).

A108541 Lesser prime factor of n-th golden semiprime.

Original entry on oeis.org

2, 3, 7, 11, 19, 23, 29, 37, 41, 67, 79, 97, 101, 103, 107, 131, 149, 163, 167, 181, 193, 227, 241, 271, 277, 283, 311, 353, 367, 379, 383, 397, 409, 419, 433, 449, 457, 487, 509, 563, 607, 613, 631, 661, 719, 733, 761, 797, 853, 883, 919, 941, 971, 997, 1031

Offset: 1

Reinhard Zumkeller, Jun 09 2005

nonn

abs(phi*a(n) - A108542(n)) < 1, where phi = golden ratio = (1+sqrt(5))/2.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001622, A084126, A108539, A108540, A108542, A108543, A108544.

f[p_] := Module[{x = GoldenRatio * p}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; q = If[x - p1 < p2 - x, p1, p2]; If[Abs[q - x] < 1, q, 0]]; seq = {}; p=1; Do[p = NextPrime[p]; If[f[p] > 0, AppendTo[seq, p]], {200}]; seq (* Amiram Eldar, Nov 28 2019 *)

a(n) = A108540(n)/A108542(n).

A108543 Primes that are factors of golden semiprimes (A108540).

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 37, 41, 47, 59, 67, 79, 97, 101, 103, 107, 109, 127, 131, 149, 157, 163, 167, 173, 181, 193, 211, 227, 241, 263, 271, 277, 283, 293, 311, 313, 353, 367, 379, 383, 389, 397, 409, 419, 433, 439, 449, 457, 487, 503, 509, 563, 571

Offset: 1

Reinhard Zumkeller, Jun 09 2005

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Union of A108541 and A108542.
Complement of A108545.
Cf. A108539, A108540, A108544.

Corrected by T. D. Noe, Oct 25 2006

A108545 Primes that are not factors of golden semiprimes (A108540).

Original entry on oeis.org

13, 43, 53, 61, 71, 73, 83, 89, 113, 137, 139, 151, 179, 191, 197, 199, 223, 229, 233, 239, 251, 257, 269, 281, 307, 317, 331, 337, 347, 349, 359, 373, 401, 421, 431, 443, 461, 463, 467, 479, 491, 499, 521, 523, 541, 547, 557, 569, 577, 587, 599, 601, 617

Offset: 1

Reinhard Zumkeller, Jun 09 2005

nonn

Complement of A108543;

abs(a(i) - a(j) * phi) > 1 for all i and j, where phi = golden ratio = (1+sqrt(5))/2.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001622, A108539, A108540, A108542, A108543, A108544.

cp's OEIS Frontend

A108542 Greater prime factor of n-th golden semiprime.

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A108541 Lesser prime factor of n-th golden semiprime.

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A108543 Primes that are factors of golden semiprimes (A108540).

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A108545 Primes that are not factors of golden semiprimes (A108540).

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