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.

Previous Showing 11-14 of 14 results.

A275715 Permutation of natural numbers: a(n) = A243071(A249823(n)).

Original entry on oeis.org

0, 1, 3, 7, 15, 31, 63, 127, 2, 255, 511, 6, 1023, 2047, 4095, 8191, 5, 16383, 14, 32767, 65535, 30, 131071, 262143, 524287, 13, 1048575, 2097151, 62, 4194303, 29, 126, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 254, 61, 11, 4, 536870911, 1073741823, 125, 2147483647, 4294967295, 27, 510, 8589934591
Offset: 1

Views

Author

Antti Karttunen, Aug 06 2016

Keywords

Comments

Note the indexing: the domain starts from 1, while the range includes also zero.

Links

Crossrefs

Inverse: A275716.
Related or similar permutations: A243071, A249823, A245611.
Cf. also A273664, A273669.

Programs

Formula

a(n) = A243071(A249823(n)).

A306331 Numbers congruent to 6 or 31 mod 38.

Original entry on oeis.org

6, 31, 44, 69, 82, 107, 120, 145, 158, 183, 196, 221, 234, 259, 272, 297, 310, 335, 348, 373, 386, 411, 424, 449, 462, 487, 500, 525, 538, 563, 576, 601, 614, 639, 652, 677, 690, 715, 728, 753, 766, 791, 804, 829, 842, 867, 880, 905
Offset: 1

Views

Author

Davis Smith, Feb 07 2019

Keywords

Comments

A007310(a(n) + 1) is always a multiple of 19.
A020639(A007310(a(n) + 1)) = 5, 7, 11, 13, 17, or 19.
It equals 5 when n is a term in A273669.
It equals 7 when n is congruent to 3 or 12 (mod 14) but not a term in A273669.
It equals 11 when n is congruent to 4 or 19 (mod 22) but not a case where it equals 5 or 7.
It equals 13 when n is congruent to 5 or 22 (mod 26) (one more than a term in A306285) but not a case where it equals 5, 7, or 11.
It equals 17 when n is congruent to 6 or 29 (mod 34) but not a case where it equals 5, 7, 11, or 13.
For all other cases, it equals 19.
a(n) and (n - 1) have the same remainder (mod 6) (see A010875).

Links

Crossrefs

Cf. A005408, A005843, A007310, A010875, A020639, A040031, A273669, A306285.

Programs

  • Maple
    seq(seq(38*i+j, j=[6, 31]), i=0..200);
  • Mathematica
    Select[Range[200], MemberQ[{6, 31}, Mod[#, 38]] &]
Union[38Range[30] - 32, 38Range[30] - 7] (* Alonso del Arte, Feb 08 2019 *)
  • PARI
    for(n=6, 905, if((n%38==6) || (n%38==31), print1(n, ", ")))
  • PARI
    Vec(x*(6 + 25*x + 7*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Feb 09 2019
  • Scala
    (6 to 1108 by 38).union(31 to 1133 by 38).sorted // Alonso del Arte, Feb 08 2019

Formula

G.f.: x*(6 + 25*x + 7*x^2) / ((1 - x)^2*(1 + x)). - Colin Barker, Feb 09 2019
a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3.
a(n) = 19*n - 10 + 3*(-1)^n. - Wesley Ivan Hurt, Mar 10 2019
a(n) = 19*n - 13 when n is odd and 19*n - 7 when n is even.
a(n) = 19*n - (A040031(n + 1) + 1).
E.g.f.: 7 + (19*x - 10)*exp(x) + 3*exp(-x). - David Lovler, Sep 10 2022

A306278 Numbers congruent to 2 or 11 mod 14.

Original entry on oeis.org

2, 11, 16, 25, 30, 39, 44, 53, 58, 67, 72, 81, 86, 95, 100, 109, 114, 123, 128, 137, 142, 151, 156, 165, 170, 179, 184, 193, 198, 207, 212, 221, 226, 235, 240, 249, 254, 263, 268, 277, 282, 291, 296, 305, 310, 319, 324, 333, 338, 347, 352, 361, 366, 375, 380, 389, 394
Offset: 1

Views

Author

Davis Smith, Feb 02 2019

Keywords

Links

Crossrefs

Cf. A007310, A010703, A020639, A047470, A091999, A273669, A306277, A306289.
Primes greater than 2 in this sequence: A045471.

Programs

  • Maple
    seq(seq(14*i+j, j=[2, 11]), i=0..28);
  • Mathematica
    Flatten[Table[{14n + 2, 14n + 11}, {n, 0, 28}]]
LinearRecurrence[{1,1,-1},{2,11,16},60] (* Harvey P. Dale, Jan 16 2023 *)
  • PARI
    for(n=2, 394, if((n%14==2) || (n%14==11), print1(n, ", ")))
  • PARI
    for(n=1,57,print1(7*n-4+(-1)^n,", "))
  • PARI
    for(n=1,500,if(n%14==2,print1(n,", "));if(n%14==11,print1(n,", "))) \\ Jinyuan Wang, Feb 03 2019
  • PARI
    Vec(x*(2 + 9*x + 3*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Mar 14 2019
  • PARI
    upto(n) = forstep(i = 2, n, [9, 5], print1(i", ")) \\ David A. Corneth, Mar 27 2019

Formula

a(n) = 7*n - A010703(n).
a(n) = 7*n - 4 + (-1)^n.
a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3.
A007310(a(n) + 1) = 7*A007310(n)
From Jinyuan Wang, Feb 03 2019: (Start)
For odd number k, a(k) = 7*k - 5.
For even number k, a(k) = 7*k - 3.
(End)
G.f.: x*(2 + 9*x + 3*x^2) / ((1 - x)^2*(1 + x)). - Colin Barker, Mar 14 2019
E.g.f.: 3 + (7*x - 4)*exp(x) + exp(-x). - David Lovler, Sep 07 2022

A306279 Numbers congruent to 3 or 18 mod 22.

Original entry on oeis.org

3, 18, 25, 40, 47, 62, 69, 84, 91, 106, 113, 128, 135, 150, 157, 172, 179, 194, 201, 216, 223, 238, 245, 260, 267, 282, 289, 304, 311, 326, 333, 348, 355, 370, 377, 392, 399, 414, 421, 436, 443, 458, 465, 480, 487, 502, 509, 524, 531, 546, 553, 568
Offset: 1

Views

Author

Davis Smith, Feb 02 2019

Keywords

Links

Crossrefs

Cf. A007310, A020639, A042948, A091999, A105398, A131555, A141850, A158459, A273669, A306277, A306289.
Primes in this sequence: A141850.

Programs

  • Maple
    seq(seq(22*i+j, j=[3, 18]), i=0..200);
  • Mathematica
    Select[Range[200], MemberQ[{3, 18}, Mod[#, 22]] &]
Flatten[Table[{22n + 3, 22n + 18}, {n, 0, 43}]] (* Alonso del Arte, Feb 18 2019 *)
  • PARI
    for(n=3, 678, if((n%22==3) || (n%22==18), print1(n, ", ")))
  • PARI
    vector(62,n,11*n-6+2*(-1)^n)
  • PARI
    Vec(x*(3 + 15*x + 4*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Feb 07 2019
  • Scala
    (3 to 949 by 22).union(18 to 942 by 22).sorted // Alonso del Arte, Feb 18 2019

Formula

a(n) = 11*n - 6 + 2*(-1)^n.
a(n) = 11*n - A105398(n + 4).
A007310(a(n) + 1) = 11*A007310(n).
From Colin Barker, Feb 07 2019: (Start)
G.f.: x*(3 + 15*x + 4*x^2) / ((1 - x)^2*(1 + x)).
a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3. (End)
E.g.f.: 4 + (11*x - 6)*exp(x) + 2*exp(-x). - David Lovler, Sep 08 2022
Previous Showing 11-14 of 14 results.

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