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.

A329898 a(n) is the position of 2*A025487(n) in A025487.

Original entry on oeis.org

2, 3, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 42, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 74, 75, 76, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100
Offset: 1

Views

Author

Antti Karttunen, Dec 24 2019

Keywords

Comments

Numbers k for which A007814(A025487(k)) > A007949(A025487(k)), i.e., numbers k for which the 2-adic valuation of A025487(k) is larger than its 3-adic valuation.
Numbers k for which A181815(k) is even.

Links

Crossrefs

Cf. A329897 (complement), A330683 (and its permutation).
Cf. A007814, A007949, A025487, A329904 (a left inverse), A329906.
Positions of even terms in A181815, zeros in A330682.

Programs

  • Mathematica
    (* First, load the function f at A025487, then: *)
With[{s = Union@ Flatten@ f@ 6}, Map[If[2 # > Max@ s, Nothing, FirstPosition[s, 2 #][[1]] ] &, s]] (* Michael De Vlieger, Jan 11 2020 *)
  • PARI
    upto_e = 64; \\ 64 -> 43608 terms.
A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980
A329898list(e) = { my(lista = List([1, 2]), i=2, u = 2^e, t, v025487); while(lista[i] != u, if(2*lista[i] <= u, listput(lista,2*lista[i]); t =
A283980(lista[i]); if(t <= u, listput(lista,t))); i++); v025487 = vecsort(Vec(lista)); lista = List([]); for(i=1,oo,if(!(t=vecsearch(v025487,2*(v025487[i]))),return(Vec(lista)), listput(lista,t))); };
v329898 = A329898list(upto_e);
A329898(n) = v329898[n];

Formula

For all n >= 1, A329904(a(n)) = n.

A330683 a(n) is the position of A283980(A025487(n)) in A025487.

Original entry on oeis.org

1, 4, 11, 9, 23, 20, 44, 41, 22, 79, 38, 73, 43, 131, 69, 124, 77, 212, 118, 72, 201, 54, 110, 129, 327, 191, 123, 312, 93, 181, 209, 493, 300, 199, 474, 154, 286, 128, 324, 725, 190, 454, 147, 272, 310, 697, 245, 434, 208, 490, 1044, 299, 671, 114, 232, 416, 469, 1008, 374, 646, 321, 721, 1481, 451, 974, 186, 359
Offset: 1

Views

Author

Antti Karttunen, Dec 26 2019

Keywords

Links

Crossrefs

Permutation of A329897.
Cf. A025487, A085089, A101296, A181815, A283980, A329898 (positive integers not in this sequence), A329904 (a left inverse), A329906, A330681.

Programs

  • Mathematica
    (* First, load the function f at A025487, then: *)
With[{s = Union@ Flatten@ f@ 10}, TakeWhile[#, # != 0 &] &@ Map[If[# > Max@ s, 0, FirstPosition[s, #][[1]] ] &[(Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1])*2^IntegerExponent[#, 2]] &, s]] (* Michael De Vlieger, Jan 11 2020 *)
  • PARI
    upto_e = 101;
A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980
A330683list(e) = { my(lista = List([1, 2]), i=2, u = 2^e, t, v025487); while(lista[i] != u, if(2*lista[i] <= u, listput(lista,2*lista[i]); t = A283980(lista[i]); if(t <= u, listput(lista,t))); i++); v025487 = vecsort(Vec(lista)); lista = List([]); for(i=1,oo,if(!(t=vecsearch(v025487,A283980(v025487[i]))),return(Vec(lista)), listput(lista,t))); };
v330683 = A330683list(upto_e);
A330683(n) = v330683[n];

Formula

a(n) = A085089(A330681(n)) = A101296(A330681(n)) = A101296(A283980(A025487(n))).
For all n >= 1, A329904(a(n)) = n.

A329901 Inverse permutation to A181815.

Original entry on oeis.org

1, 2, 4, 3, 9, 6, 22, 5, 11, 13, 54, 8, 114, 29, 20, 7, 246, 15, 488, 17, 43, 66, 948, 12, 38, 140, 23, 36, 1809, 27, 3327, 10, 93, 290, 72, 19, 6020, 570, 186, 24, 10624, 55, 18246, 83, 41, 1090, 30726, 16, 128, 49, 376, 168, 51148, 30, 147, 47, 718, 2057, 84074, 34, 135598, 3743, 77, 14, 279, 112, 216398, 343, 1348, 89, 340886, 26, 529051, 6715, 69, 660
Offset: 1

Views

Author

Antti Karttunen, Dec 23 2019

Keywords

Links

Crossrefs

Cf. A181815 (inverse permutation).
Cf. A025487, A108951, A243071, A329906.

Formula

a(n) = A329906(A243071(n)).
For all n >= 1, A025487(a(n)) = A108951(n).

A329905 a(1) = 0; a(2) = 1; and for n > 2, a(n) = A330682(n) + 2*a(A329904(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 12, 7, 16, 5, 24, 14, 32, 10, 48, 28, 64, 20, 13, 96, 15, 9, 56, 128, 40, 26, 192, 30, 18, 112, 256, 80, 52, 384, 60, 36, 11, 224, 512, 25, 160, 29, 17, 104, 768, 120, 72, 22, 448, 1024, 50, 320, 31, 58, 34, 208, 1536, 240, 144, 44, 896, 2048, 100, 640, 62, 116, 68, 21, 416, 3072, 27, 49, 480, 288, 88, 57
Offset: 1

Views

Author

Antti Karttunen, Dec 24 2019

Keywords

Comments

Note the indexing: domain begins from one, but the range contains also zero.

Links

Crossrefs

Cf. A329906 (inverse permutation).
Cf. A000035, A025487, A061394, A181815, A243071, A329897, A329898, A329904, A329907, A330682.

Programs

Formula

a(1) = 0; a(2) = 1; and for n > 2, if A181815(n) is odd, a(n) = 1 + 2*a(A329904(n)), otherwise a(n) = 2*a(A329904(n)).
a(n) = A243071(A181815(n)).
For all n >= 1, A000120(a(n)) = A061394(n).
For all n >= 2, A070939(a(n)) = A329907(n).

A341352 Inverse permutation to A341351.

Original entry on oeis.org

1, 2, 4, 9, 3, 22, 54, 6, 114, 246, 13, 488, 11, 5, 948, 1809, 29, 20, 3327, 66, 6020, 10624, 8, 18246, 38, 140, 30726, 43, 290, 51148, 84074, 17, 93, 135598, 570, 216398, 340886, 15, 72, 529051, 7, 814237, 186, 1090, 1240172, 147, 2057, 376, 1874464, 36, 2817289
Offset: 1

Views

Author

Antti Karttunen and Michael De Vlieger, Feb 14 2021

Keywords

Links

Crossrefs

Cf. A064216, A064989, A329898, A329901, A329906, A330683.
Cf. A341351 (inverse).

Formula

a(n) = A329901(A064216(n)).
Showing 1-5 of 5 results.

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