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.

A102332 Initial prime p introducing a prime sextuplet of consecutive primes as follows: {p, p+10, p+18, p+28, p+36, p+46} with the corresponding prime-difference-pattern is {10,8,10,8,10}.

Original entry on oeis.org

37861, 39181, 324763, 692743, 810391, 945331, 1047961, 1429573, 1513573, 1540813, 1799071, 3463573, 3861223, 3979201, 4536121, 4641001, 5154343, 5445403, 5874853, 7851583, 8820793, 8961373, 8976403, 9302113, 9673351, 10323133, 11074033, 11136883, 11899333, 13505983
Offset: 1

Views

Author

Labos Elemer, Jan 06 2005

Keywords

Comments

A generalization of primes displayed in A022008.

Crossrefs

Programs

  • Mathematica
    tm=TimeUsed[];ta={{0}};Do[g=n;d1=10;d2=8;d3=10;d4=8;d5=10; s1=Prime[n+1]-Prime[n];s2=Prime[n+2]-Prime[n+1]; s3=Prime[n+3]-Prime[n+2];s4=Prime[n+4]-Prime[n+3]; s5=Prime[n+5]-Prime[n+4];If[Equal[s1, d1]&&Equal[s2, d2]&& Equal[s3, d3]&&Equal[s4, d4]&&Equal[s5, d5], Print[{Prime[n], s1, s2, s3, s4, s5}];ta=Append[ta, Prime[n]]], {n, 1, 10000000}] {ta=Delete[ta, 1], {d1, d2}} {g, TimeUsed[]-tm}
    Transpose[Select[Partition[Prime[Range[650000]],6,1],Differences[#]=={10,8,10,8,10}&]][[1]] (* Harvey P. Dale, Oct 18 2013 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7, p5 = 11); forprime(p6 = 13, lim, if(p2 - p1 == 10 && p3 - p2 == 8 && p4 - p3 == 10 && p5 - p4 == 8 && p6 - p5 == 10, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5; p5 = p6);} \\ Amiram Eldar, Feb 18 2025

Formula

a(n) == 1 (mod 6). - Amiram Eldar, Feb 18 2025

Extensions

Definition corrected by Harvey P. Dale, Oct 18 2013

A067141 Primes p beginning consecutive prime-difference pattern as follows: p, (16, 2, 16, 2), p+36.

Original entry on oeis.org

225733, 819373, 830293, 856993, 895633, 924793, 1138393, 1210003, 1214623, 1353223, 1526053, 2051443, 2183773, 2298853, 2345443, 3169723, 3254773, 3287293, 3539743, 3675613, 3847603, 4630063, 4633003, 5137003, 5238403
Offset: 1

Views

Author

Labos Elemer, Jan 02 2002

Keywords

Examples

			First term a(1)=p(20082)=225773; it is followed by 225789, 225791, 225807, 225809=p(20086) primes, where the 4 corresponding consecutive differences equal {16, 2, 16, 2}. See analogous cases A022008, A067140.
		

Crossrefs

Programs

  • Mathematica
    d[x_] := Prime[x+1]-Prime[x] Do[If[Equal[d[n], 16]&&Equal[d[n+1], 2]&& Equal[d[n+2], 16]&&Equal[d[n+3], 2], k=k+1; Print[Prime[n]]], {n, 1, 10000000}]
    Select[Partition[Prime[Range[400000]],5,1],Differences[#]=={16,2,16,2}&][[All,1]] (* Harvey P. Dale, Jan 01 2018 *)

A102333 Initial terms of quartets of consecutive primes as follows: {p, p+16, p+24, p+40}. The corresponding difference-pattern is {16,8,16}.

Original entry on oeis.org

108247, 121507, 166783, 169567, 178207, 216133, 257053, 258763, 272863, 274123, 372613, 383533, 384343, 396157, 413143, 501577, 562477, 577153, 581353, 635293, 721267, 727273, 738937, 769903, 908113, 917713, 932497, 937903, 965467, 980377, 989647, 1008547, 1126537
Offset: 1

Views

Author

Labos Elemer, Jan 06 2005

Keywords

Comments

A generalization of A052378.

Crossrefs

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[78000]],4,1],Differences[#] == {16,8,16}&]][[1]] (* Harvey P. Dale, Mar 18 2012 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5); forprime(p4 = 7, lim, if(p2 - p1 == 16 && p3 - p2 == 8 && p4 - p3 == 16, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4);} \\ Amiram Eldar, Feb 18 2025

Formula

a(n) == 1 (mod 6). - Amiram Eldar, Feb 18 2025

A102334 Initial terms of quintuplets of consecutive primes as follows: {p, p+16, p+24, p+40, p+48}. The corresponding difference-pattern is {16,8,16,8}.

Original entry on oeis.org

272863, 274123, 372613, 1394893, 1634293, 2380423, 3846373, 5298523, 5358013, 5797903, 6741913, 7554823, 7647643, 7716103, 7738153, 8241463, 8358283, 9710473, 9859783, 12454333, 12510193, 12796423, 13710133, 14477893, 15162493, 15186583, 15263503, 15603853, 16438243, 16771933, 17913283, 18957973, 19373623
Offset: 1

Views

Author

Labos Elemer, Jan 06 2005

Keywords

Comments

A generalization of A022007.

Crossrefs

Programs

  • Mathematica
    Select[Partition[Prime[Range[1233300]], 5, 1], Differences[#] == {16, 8, 16, 8} &][[;;, 1]] (* Amiram Eldar, Feb 18 2025 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 16 && p3 - p2 == 8 && p4 - p3 == 16 && p5 - p4 == 8, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 18 2025

Formula

a(n) == 13 (mod 30). - Amiram Eldar, Feb 18 2025

Extensions

Missing terms a(1)-a(11) inserted by Amiram Eldar, Feb 18 2025

A102335 Initial terms of sextuplets of consecutive primes as follows: {p, p+16, p+24, p+40, p+48, p+64}. The corresponding difference-pattern is {16,8,16,8,16}.

Original entry on oeis.org

12454333, 21228553, 25131193, 38589673, 41426353, 46254253, 56564623, 60498133, 61151863, 96691213, 158497153, 169760713, 182960473, 201513133, 226086283, 236031463, 253806913, 290686483, 305472373, 344550643, 369110983, 380973253, 421335883, 445537333, 461955763
Offset: 1

Views

Author

Labos Elemer, Jan 06 2005

Keywords

Comments

A generalization of A022008. The generalized pattern of consecutive prime-differences is {6a+4, 6b+2, 6c+4, 6d+2, 6e+4} with a = c = e = 2, b = d = 1.

Crossrefs

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[20000000]],6,1],Differences[#] == {16,8,16,8,16}&]][[1]] (* Harvey P. Dale, Nov 08 2011 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7, p5 = 11); forprime(p6 = 13, lim, if(p2 - p1 == 16 && p3 - p2 == 8 && p4 - p3 == 16 && p5 - p4 == 8 && p6 - p5 == 16, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5; p5 = p6);} \\ Amiram Eldar, Feb 18 2025

Formula

a(n) == 73 (mod 210). - Amiram Eldar, Feb 18 2025
Showing 1-5 of 5 results.