cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A303216 A(n,k) is the n-th Fibonacci number with exactly k prime factors (counted with multiplicity); square array A(n,k), n>=1, k>=1, read by antidiagonals.

Original entry on oeis.org

2, 21, 3, 8, 34, 5, 6765, 610, 55, 13, 2584, 196418, 987, 377, 89, 144, 701408733, 317811, 10946, 4181, 233, 832040, 102334155, 1134903170, 2178309, 75025, 17711, 1597, 86267571272, 267914296, 12586269025, 365435296162, 32951280099, 3524578, 121393, 28657
Offset: 1

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Author

Alois P. Heinz, Apr 19 2018

Keywords

Examples

			Square array A(n,k) begins:
    2,    21,       8,         6765,           2584,                 144, ...
    3,    34,     610,       196418,      701408733,           102334155, ...
    5,    55,     987,       317811,     1134903170,         12586269025, ...
   13,   377,   10946,      2178309,   365435296162,      10610209857723, ...
   89,  4181,   75025,  32951280099,  6557470319842,    2111485077978050, ...
  233, 17711, 3524578, 139583862445, 72723460248141, 7540113804746346429, ...
		

Crossrefs

Columns k=1-2 give: A005478, A053409.
Row n=1 gives A072397.

Programs

  • Maple
    F:= combinat[fibonacci]: with(numtheory):
    A:= proc() local h, p, q; p, q:= proc() [] end, 2;
          proc(n, k)
            while nops(p(k))
    				
  • Mathematica
    A[n_, k_] := Module[{F = Fibonacci, h, p, q = 2}, p[_] = {}; While[ Length[p[k]] < n, q = q+1; h = PrimeOmega[F[q]]; p[h] = Append[p[h], F[q]]]; p[k][[n]]];
    Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 10}] // Flatten (* Jean-François Alcover, Feb 05 2021, after Alois P. Heinz *)

Formula

A(n,k) = A000045(A303215(n,k)).
A001222(A(n,k)) = k.

A072396 Index of smallest Fibonacci number with n prime factors when counted with multiplicity.

Original entry on oeis.org

3, 8, 6, 20, 18, 12, 30, 54, 24, 36, 138, 48, 84, 72, 108, 96, 210, 120, 276, 168, 216, 252, 288, 240, 336, 570, 384, 420, 360, 576, 480, 540, 504, 660, 600, 672, 990, 720, 792, 840, 1152, 1140
Offset: 1

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Author

Shyam Sunder Gupta, Jul 21 2002

Keywords

Comments

1452 < a(43) <= 1596, a(44) = 1296, a(45) = 1368, a(46) = 1080, a(47) = 1200, a(48) <= 1728. - Daniel Suteu, Jan 19 2023

Examples

			a(3) = 6 since the 6th Fibonacci number 8 has 3 prime factors.
		

Crossrefs

Row n=1 of A303215.

Programs

  • PARI
    a(n) = my(k=1); while (bigomega(fibonacci(k)) != n, k++); k; \\ Michel Marcus, Aug 26 2020

Extensions

a(17)-a(24) from Alois P. Heinz, Apr 10 2018
a(25)-a(42) from Amiram Eldar, Aug 26 2020

A359876 a(n) is the smallest tribonacci number (A000073) with exactly n prime factors (counted with multiplicity).

Original entry on oeis.org

1, 2, 4, 44, 24, 5768, 504, 10562230626642, 3136, 7046319384, 615693474, 53798080, 4680045560037375, 35574238430251050319992, 4659412488735286161146176, 23523635785731871586396890786299881280, 79932289960699059086717998848
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 16 2023

Keywords

Examples

			a(5) = 5768, because 5768 is a tribonacci number with 5 prime factors (counted with multiplicity) {2, 2, 2, 7, 103} and this is the smallest such number.
		

Crossrefs

A359877 a(n) is the smallest tetranacci number (A000078) with exactly n prime factors (counted with multiplicity).

Original entry on oeis.org

1, 2, 4, 8, 56, 108, 5536, 28074040, 39648, 147312, 18566888967365603514688, 9966792788887776, 2775641472, 2505471397838180985096739296, 1445523368993397560000765219760086502994234237205516083525719052320, 44092571484448511101335177770183225655413760
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 16 2023

Keywords

Examples

			a(6) = 5536, because 5536 is a tetranacci number with 6 prime factors (counted with multiplicity) {2, 2, 2, 2, 2, 173} and this is the smallest such number.
		

Crossrefs

A359880 a(n) is the smallest Fibonacci n-step number with exactly n prime factors (counted with multiplicity).

Original entry on oeis.org

21, 44, 56, 120, 1936, 2000, 2035872, 32512, 265816832, 523008, 8565824256, 67047424, 134156288, 1073463296, 35176050802688, 8589344768, 562914520154112, 18013762856812544, 144112508021833728, 2305819919496904704, 1099509006336, 137438822400
Offset: 2

Views

Author

Ilya Gutkovskiy, Jan 16 2023

Keywords

Examples

			a(3) = 44, because 44 is a tribonacci number with 3 prime factors (counted with multiplicity) {2, 2, 11} and this is the smallest such number.
		

Crossrefs

Showing 1-5 of 5 results.