A108543 -id:A108543 - 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).

A108544 Primes that are factors of distinct golden semiprimes (A108540).

Original entry on oeis.org

3, 11, 37, 67, 163, 167, 241, 271, 367, 449, 457, 613, 661, 1613, 1979, 2069, 2137, 2221, 2347, 2351, 2381, 2399, 2477, 2633, 2749, 2837, 3011, 3449, 3593, 3671, 3797, 3911, 3943, 4001, 4049, 4079, 4241, 4999, 5147, 5261, 5711, 5981, 6337, 6379, 6619

Offset: 1

Reinhard Zumkeller, Jun 09 2005

nonn

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

Intersection of A108541 and A108542.

Cf. A108540, A108543.

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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A108544 Primes that are factors of distinct golden semiprimes (A108540).

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

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