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.

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A253705 Indices of primes in the 8th-order Fibonacci number sequence, A079262.

Original entry on oeis.org

9, 17, 25, 125, 350, 1322, 108935, 199528
Offset: 1

Views

Author

Robert Price, Jan 09 2015

Keywords

Comments

a(9) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262.

Programs

  • Mathematica
    a={0,0,0,0,0,0,0,1}; step=8; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Flatten[Position[LinearRecurrence[{1,1,1,1,1,1,1,1},{0,0,0,0,0,0,0,1},200000],?PrimeQ]]-1 (* The program takes a long time to run *) (* _Harvey P. Dale, Apr 26 2018 *)
  • PARI
    lista(nn) = {gf = x^7/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8); for (n=0, nn, if (isprime(polcoeff(gf+O(x^(n+1)), n)), print1(n, ", ")););} \\ Michel Marcus, Jan 12 2015

A187833 Rank transform of the sequence floor(3n/2-1/2); complement of A187834.

Original entry on oeis.org

1, 3, 5, 6, 9, 10, 12, 14, 16, 17, 19, 21, 23, 25, 27, 28, 30, 32, 34, 36, 38, 39, 41, 43, 45, 46, 49, 50, 52, 54, 56, 58, 59, 61, 63, 65, 67, 68, 70, 72, 74, 76, 78, 79, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 101, 103, 105, 107, 108, 111, 112, 114, 116, 118, 119, 121, 123, 125, 127, 129, 130, 133, 134, 136, 138, 140, 141, 143, 145, 147, 149
Offset: 1

Views

Author

Clark Kimberling, Mar 13 2011

Keywords

Comments

A187833 is the rank transform of the sequence A001631 of positive integers not divisible by 3. For a discussion of rank transforms, see A187224.

Crossrefs

Cf. A187224, A187834.

Programs

  • Mathematica
    seqA = Table[Floor[3n/2-1/2], {n, 1, 220}]
seqB = Table[n, {n, 1, 220}];(*A000027*)
jointRank[{seqA_,
   seqB_}] := {Flatten@Position[#1, {_, 1}],
    Flatten@Position[#1, {_, 2}]} &[
  Sort@Flatten[{{#1, 1} & /@ seqA, {#1, 2} & /@ seqB}, 1]];
limseqU =
 FixedPoint[jointRank[{seqA, #1[[1]]}] &,
   jointRank[{seqA, seqB}]][[1]] (*A187833*)
Complement[Range[Length[seqA]], limseqU]  (*A187834*)
(*by Peter J. C. Moses, Mar 13 2011*)

A232564 Inverse permutation of the sequence of positive integers at A232563.

Original entry on oeis.org

1, 2, 4, 3, 6, 11, 21, 5, 9, 17, 33, 8, 15, 29, 56, 7, 13, 25, 48, 12, 23, 44, 85, 22, 42, 81, 156, 41, 79, 152, 293, 10, 19, 37, 71, 18, 35, 67, 129, 34, 65, 125, 241, 64, 123, 237, 457, 16, 31, 60, 115, 30, 58, 111, 214, 57, 109, 210, 405, 108, 208, 401
Offset: 1

Views

Author

Clark Kimberling, Nov 26 2013

Keywords

Links

Crossrefs

Cf. A232559, A232563.

Programs

  • Mathematica
    z = 8; g[1] = {1}; g[2] = {2, 4}; g[n_] := Riffle[g[n - 1] + 1, 4 g[n - 1]]; j[2] = Join[g[1], g[2]]; j[n_] := Join[j[n - 1], g[n]]; g1[n_] := DeleteDuplicates[DeleteCases[g[n], Alternatives @@ j[n - 1]]]; g1[1] = g[1]; g1[2] = g[2]; t = Flatten[Table[g1[n], {n, 1, z}]]  (* A232563 *)
Table[Length[g1[n]], {n, 1, z}]  (* A001631 *)
t1 = Flatten[Table[Position[t, n], {n, 1, 200}]]  (* A232564 *)

A253333 Primes in the 7th-order Fibonacci numbers A060455.

Original entry on oeis.org

7, 13, 97, 193, 769, 1531, 3049, 6073, 12097, 24097, 95617, 379399, 2998753, 187339729, 373174033, 2949551617, 184265983633, 731152932481, 88025699967469825543, 175344042716296888429, 4979552865927484193343796114081304399449
Offset: 1

Views

Author

Robert Price, Dec 30 2014

Keywords

Comments

a(22) is too large to display here. It has 53 digits and is the 180th term in A060455.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318.

Programs

  • Mathematica
    a={1,1,1,1,1,1,1}; step=7; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[7]]=sum]; lst
With[{c=PadRight[{},7,1]},Select[LinearRecurrence[c,c,150],PrimeQ]] (* Harvey P. Dale, May 08 2015 *)
  • PARI
    lista(nn) = {gf = ( -1+x^2+2*x^3+3*x^4+4*x^5+5*x^6 ) / ( -1+x+x^2+x^3+x^4+x^5+x^6+x^7 ); for (n=0, nn, if (isprime(p=polcoeff(gf+O(x^(n+1)), n)), print1(p, ", ")););} \\ Michel Marcus, Jan 11 2015

A254412 Indices of primes in the 8th-order Fibonacci number sequence, A123526.

Original entry on oeis.org

11, 13, 15, 24, 30, 33, 57, 104, 121, 132, 149, 158, 178, 220, 295, 389, 1070, 1101, 1373, 1761, 1778, 2333, 2731, 4541, 5189, 5237, 5738, 8025, 8787, 10561, 11783, 13435, 14638, 15337, 20985, 21722, 24770, 31009, 57367, 65877, 129773, 134630, 167020
Offset: 1

Views

Author

Robert Price, Jan 30 2015

Keywords

Comments

a(44) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A123526, A254413.

Programs

  • Mathematica
    a={1,1,1,1,1,1,1,1}; step=8; lst={}; For[n=step+1,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A254413 Primes in the 8th-order Fibonacci numbers A123526.

Original entry on oeis.org

29, 113, 449, 226241, 14307889, 113783041, 1820091580429249, 233322881089059894782836851617, 29566627412209231076314948970028097, 59243719929958343565697204780596496129, 7507351981539044730893385057192143660843521
Offset: 1

Views

Author

Robert Price, Jan 30 2015

Keywords

Comments

a(12) is too large to display here. It has 46 digits and is the 158th term in A123526.

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318, A079262, A253705, A123526, A254412.

Programs

  • Mathematica
    a={1,1,1,1,1,1,1,1}; step=8; lst={}; For[n=step+1,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Select[With[{lr=PadRight[{},8,1]},LinearRecurrence[lr,lr,200]],PrimeQ] (* Harvey P. Dale, Dec 03 2022 *)

A299399 a(n) = a(n-1)*a(n-2)*a(n-3)*a(n-4); a(0..3) = (1, 1, 2, 3).

Original entry on oeis.org

1, 1, 2, 3, 6, 36, 1296, 839808, 235092492288, 9211413321697223245824, 2356948205087252000835395074931259831484416, 4286423488783965214900384842824017360544199884413056912194095171350270745233063936
Offset: 0

Views

Author

M. F. Hasler, Apr 22 2018

Keywords

Comments

A variant of A000336 which uses initial values (1,2,3,4).
A multiplicative variant of the tetranacci sequences A000078, A001631 and other variants.

Links

Crossrefs

Cf. A000336 (variant starting 1,2,3,4).
Cf. A000301 (order 2 variant), A000308 (order 3 variant).
Subsequence of A003586 (3-smooth numbers).
Cf. A000078, A001631 (additive variants).

Programs

  • Mathematica
    nxt[{a_,b_,c_,d_}]:={b,c,d,a b c d}; NestList[nxt,{1,1,2,3},13][[All,1]] (* Harvey P. Dale, Jun 09 2022 *)
  • PARI
    A299399(n,a=[1,1,2,3,6])={for(n=5,n,a[n%#a+1]=a[(n-1)%#a+1]^2\a[n%#a+1]);a[n%#a+1]}

Formula

a(n) = a(n-1)^2 / a(n-5) for n > 4.
a(n) = 2^A001631(n)*3^A000078(n).

A303264 Indices of primes in tetranacci sequence A000078.

Original entry on oeis.org

5, 9, 13, 14, 38, 58, 403, 2709, 8419, 14098, 31563, 50698, 53194, 155184
Offset: 1

Views

Author

M. F. Hasler, Apr 18 2018

Keywords

Comments

T = A000078 is defined by T(n) = Sum_{k=1..4} T(n-k), T(3) = 1, T(n) = 0 for n < 3.
The largest terms correspond to unproven probable primes T(a(n)).

Crossrefs

Cf. A000045, A000073, A000078, A001591, A001592, A122189 (or A066178), ... (Fibonacci, tribonacci, tetranacci numbers).
Cf. A005478, A092836, A104535, A105757, A105759, A105761, ... (primes in Fibonacci numbers and above generalizations).
Cf. A001605, A303263, A303264, A248757, A249635, ... (indices of primes in A000045, A000073, A000078, ...).
Cf. A247027: Indices of primes in the tetranacci sequence A001631 (starting 0, 0, 1, 0...), A104534 (a variant: a(n) - 2), A105756 (= A248757 - 3), A105758 (= A249635 - 4).

Programs

  • PARI
    a(n,N=5,S=vector(N,i,i>N-2))={for(i=N,oo,ispseudoprime(S[i%N+1]=2*S[(i-1)%N+1]-S[i%N+1])&&!n--&&return(i))}

Formula

a(n) = A104534(n) + 2.

A382478 Number of palindromic binary strings of length n having no 4-runs of 1's.

Original entry on oeis.org

1, 2, 2, 4, 3, 7, 6, 14, 12, 27, 23, 52, 44, 100, 85, 193, 164, 372, 316, 717, 609, 1382, 1174, 2664, 2263, 5135, 4362, 9898, 8408, 19079, 16207, 36776, 31240, 70888, 60217, 136641, 116072, 263384, 223736, 507689, 431265, 978602, 831290, 1886316, 1602363, 3635991, 3088654, 7008598, 5953572
Offset: 0

Views

Author

R. J. Mathar, Mar 28 2025

Keywords

Links

Crossrefs

Cf. A001630 (bisection), A001631 (bisection).
Cf. A123231 (2-runs), A001590 (3-runs), A251653 (5-runs), A382479 (6-runs).

Programs

  • Magma
    m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(-(x^2+1)*(x^5+2*x+1) / (-1+x^2+x^4+x^6+x^8))); // Vincenzo Librandi, May 19 2025
  • Mathematica
    LinearRecurrence[{0,1,0,1,0,1,0,1},{1,2,2,4,3,7,6,14},50] (* Vincenzo Librandi, May 19 2025 *)

Formula

G.f.: -(x^2+1)*(x^5+2*x+1)/(-1+x^2+x^4+x^6+x^8).

A248700 Indices of primes in the Heptanacci numbers sequence A122189.

Original entry on oeis.org

8, 14, 22, 102495, 130447, 173590
Offset: 1

Views

Author

Robert Price, Dec 02 2014

Keywords

Comments

a(7) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A122189.

Programs

  • Mathematica
    a={0,0,0,0,0,0,1}; For[n=7, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[7]]=sum]
Previous Showing 21-30 of 41 results. Next

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