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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A090836 Numbers n such that 6*n+5, 6*n+11, 6*n+17, 6*n+23 are consecutive primes.

Original entry on oeis.org

41, 896, 1051, 2106, 2241, 2456, 2631, 2911, 3886, 4361, 9346, 10366, 12586, 13131, 13796, 14071, 14896, 15736, 15876, 17451, 19291, 20091, 20166
Offset: 1

Views

Author

Pierre CAMI, Dec 09 2003

Keywords

Examples

			6*41+5=251, 6*41+11=257, 6*41+17=263, 6*41+23=269; 251,257,263,269 are consecutive primes.

Links

Crossrefs

Cf. A033451, A090832, A090833, A090834, A090835, A090837, A090838, A090839.

Programs

  • Mathematica
    Select[(#-5)/6&/@Transpose[Select[Partition[Prime[Range[11500]],4,1], Union[Differences[#]]=={6}&]][[1]],IntegerQ] (* Harvey P. Dale, Nov 18 2013 *)

A210683 Primes p such that p, p+60, p+120, p+180 are consecutive primes.

Original entry on oeis.org

253444777, 271386581, 286000489, 415893013, 475992773, 523294549, 620164949, 794689481, 838188877, 840725323, 846389227, 884106599, 884951807, 908725507, 941796223, 952288331, 971614151, 1002290693, 1003166771, 1006976797, 1053792359, 1097338313, 1163141201
Offset: 1

Views

Author

Zak Seidov, May 09 2012

Keywords

Comments

Subsequence of A089234 which itself is a subsequence of A126771:
a(1) = 253444777 = A089234(417) = A126771(81526),
a(36) = 1998782563 = A089234(5579) = A126771(788920).

Links

Crossrefs

Cf. A089234, A126771.
Analogous sequences (start of CPAP-4, with common difference in square brackets): A033451 [6], A033447 [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36], A058323 [42], A067388 [48], A259224 [54].
Cf. A054800: union of all sequences of this type (start of CPAP-4).

Programs

  • PARI
    A210683(n, p=2, v=1, g=60, c, o)={forprime(q=p+1, , if(p+g!=p=q, next, q!=o+2*g, c=2, c++>3, v&& print1(o-g", "); n--||break); o=q-g); o-g} \\ Can be used as next(p)=A210683(1, p) to get the next term, e.g.:
p=0; A210683_vec=vector(10,i,p=A210683(1,p)) \\ Will take a long time! - M. F. Hasler, Oct 26 2018

A052160 Isolated prime difference equals 6: primes prime(k) such that d(k) = prime(k+1) - prime(k) = 6 but neither d(k+1) nor d(k-1) is 6.

Original entry on oeis.org

23, 31, 61, 73, 83, 131, 233, 271, 331, 353, 383, 433, 443, 503, 541, 571, 677, 751, 991, 1013, 1033, 1063, 1231, 1283, 1291, 1321, 1433, 1453, 1493, 1543, 1553, 1601, 1613, 1621, 1657, 1777, 1861, 1973, 1987, 2011, 2063, 2131, 2207, 2333, 2341, 2351
Offset: 1

Views

Author

Labos Elemer, Jan 25 2000

Keywords

Comments

Consecutive primes 17, 19, 23, 29, 31 give the pattern of first differences 2, 4, 6, 2 in which the neighboring differences of 6 are not equal to 6.
a(n) - 6 can be prime but not the prime immediately previous to a(n); e.g., 23 - 6 = 17, but the prime 19 lies between the two primes 17 and 23.

Links

Crossrefs

Cf. A001223, A033451, A047948.

Programs

  • Maple
    N:= 3000: # to get all terms <= N
Primes:= select(isprime, [seq(i,i=3..N,2)]):
d:= Primes[2..-1]-Primes[1..-2]:
R:= select(t -> d[t] = 6 and d[t+1] <> 6 and d[t-1] <> 6, [$2..nops(d)-1]):
Primes[R]; # Robert Israel, May 29 2018
  • PARI
    lista(nn) = {vp = primes(nn); vd = vector(#vp-1, k, vp[k+1] - vp[k]); for (i=2, #vd, if ((vd[i] == 6) && (vd[i-1] !=6) && (vd[i+1] != 6), print1(vp[i], ", ")););} \\ Michel Marcus, May 29 2018

A090833 Numbers n such that 6n+5, 6n+11, 6n+17, 6n+23 are consecutive primes or 6n+1, 6n+7, 6n+13, 6n+19 are consecutive primes.

Original entry on oeis.org

41, 290, 550, 850, 896, 1051, 1060, 2106, 2241, 2456, 2631, 2650, 2911, 3035, 3245, 3886, 4361, 5015, 5105, 8935, 9346, 10366, 10615, 11890, 12586, 12925, 13131, 13485, 13796, 13905, 14071, 14850, 14896, 15215, 15736, 15876, 15985, 17451, 17560
Offset: 1

Views

Author

Pierre CAMI, Dec 09 2003

Keywords

Links

Crossrefs

Cf. A033451, A090832, A090834, A090835, A090836, A090837, A090838, A090839.

Programs

  • Mathematica
    Select[Range[20000],(PrimeQ[6#+5]&&Differences[NestList[ NextPrime[ #]&, 6 #+5,3]] =={6,6,6})||(PrimeQ[6#+1]&&Differences[NestList[NextPrime[#]&,6 #+1,3]]=={6,6,6})&] (* Harvey P. Dale, Sep 23 2016 *)
  • PARI
    p=2;q=3;r=5;forprime(s=7,1e5,if(s-p==18&&s-q==12&&s-r==6,print1(p\6", "));p=q;q=r;r=s) \\ Charles R Greathouse IV, Dec 27 2011

Extensions

a(19) from Charles R Greathouse IV, Dec 27 2011

A090834 Primes p such that p, p+6, p+12, p+18 are consecutive primes and p=6*k+5 for some k.

Original entry on oeis.org

251, 5381, 6311, 12641, 13451, 14741, 15791, 17471, 23321, 26171, 56081, 62201, 75521, 78791, 82781, 84431, 89381, 94421, 95261, 104711, 115751, 120551, 121001, 154061, 162251, 163841, 179801, 185051, 187361, 191021, 206021, 214451, 222311, 226631, 243521
Offset: 1

Views

Author

Pierre CAMI, Dec 09 2003

Keywords

Examples

			251,257,263,269 are consecutive primes,257=251+6,263=251+12,269=251+18 and 251=6*41+5

Links

Crossrefs

Cf. A033451, A090832, A090833, A090835, A090836, A090837, A090838, A090839.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[30000]],4,1],Differences[#]=={6,6,6}&&IntegerQ[(#[[1]]-5)/6]&]][[1]] (* Harvey P. Dale, Dec 12 2015 *)

Extensions

More terms from Harvey P. Dale, Dec 12 2015

A090837 Primes p such that p, p+6, p+12, p+18 are consecutive primes and p = 6*k+1 for some k.

Original entry on oeis.org

1741, 3301, 5101, 6361, 15901, 18211, 19471, 30091, 30631, 53611, 63691, 71341, 77551, 80911, 83431, 89101, 91291, 95911, 105361, 105601, 108631, 119551, 120811, 130681, 141061, 144241, 152941, 172981, 186871, 206191, 218131, 228841, 230221, 252151, 263071, 280921, 285451
Offset: 1

Views

Author

Pierre CAMI, Dec 09 2003

Keywords

Examples

			1741, 1747, 1753, 1759 are consecutive primes, 1747 = 1741 + 6, 1753 = 1741 + 12, 1759 = 1741 + 18 and 1741 = 6 * 290 + 1.

Links

Crossrefs

Cf. A033451, A090832, A090833, A090834, A090835, A090836, A090838, A090839.

Programs

  • Maple
    filter:= p -> isprime(p) and nextprime(p) = p+6 and nextprime(p+6)=p+12 and nextprime(p+12)=p+18:
select(filter, [seq(i,i=1..10^6,6)]); # Robert Israel, Nov 11 2020
  • PARI
    isok(p) = my(q,r,s); isprime(p) && ((p % 6) == 1) && ((q=nextprime(p+1)) == p+6) && ((r=nextprime(q+1)) == p+12) && ((s=nextprime(r+1)) == p+18); \\ Michel Marcus, Sep 20 2019

Extensions

More terms from Michel Marcus, Sep 20 2019

A090838 Numbers n such that p(n),p(n)+6,p(n)+12,p(n)+18 are consecutive primes and p(n)=6*k+1 for some k, where p(n) denotes n-th prime.

Original entry on oeis.org

271, 464, 682, 829, 1853, 2086, 2209, 3253, 3303, 5463, 6386, 7064, 7620, 7918, 8145, 8631, 8828, 9243, 10052, 10074, 10329, 11257, 11368, 12223, 13100, 13359, 14105, 15751, 16909, 18481, 19455, 20332, 20456, 22213, 23071, 24510, 24874, 25420, 25595, 26233
Offset: 1

Views

Author

Pierre CAMI, Dec 09 2003

Keywords

Examples

			p(271)=1741: 1741,1747,1753,1759 are consecutive primes,1747=1741+6,1753=1741+12,1759=1741+18 and 1741=6*290+1

Links

Crossrefs

Cf. A033451, A090832, A090833, A090834, A090835, A090836, A090837, A090839.

Programs

  • Mathematica
    PrimePi/@Transpose[Select[Partition[Prime[Range[50000]],4,1], Differences[ #] == {6,6,6}&&Mod[#[[1]],6]==1&]][[1]] (* Harvey P. Dale, Nov 04 2015 *)

Extensions

More terms from Harvey P. Dale, Nov 04 2015

A259224 Initial primes in sets of 4 consecutive primes with common gap 54.

Original entry on oeis.org

400948369, 473838319, 583946599, 678953059, 816604199, 972598819, 1136526949, 1466715139, 1475790529, 1499794999, 1502149559, 1610895679, 1643313869, 1673057219, 1686181579, 1845792019, 1867046639, 1907478889, 1992202439, 2011077869, 2030490479, 2207714969
Offset: 1

Views

Author

Zak Seidov, Jun 21 2015

Keywords

Comments

All terms are == {19,29} mod 30.

Links

Crossrefs

Start of CPAP-4 with given common difference (in square brackets): A033451 [6], A033447 [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36], A058323 [42], A067388 [48], A259224 [this: 54], A210683 [60].
Subsequence of A054800: start of a CPAP-4 with arbitrary common difference.

Programs

  • PARI
    A259224(n, p=2, v=1, g=54, c, o)={forprime(q=p+1, , if(p+g!=p=q, next, q!=o+2*g, c=2, c++>3, v&& print1(o-g", "); n--||break); o=q-g); o-g} \\ Can be used as next(p)=A259224(1,p+1) to get the next term, e.g.:
p=0; A259224_vec=vector(10,i,p=A259224(1,p+1)) \\ Will be slow! - M. F. Hasler, Oct 26 2018

A052190 Primes p such that p, p+24, p+48 are consecutive primes.

Original entry on oeis.org

16763, 40039, 42509, 96353, 98573, 104183, 119243, 123863, 160093, 161783, 169259, 181789, 185243, 208529, 209719, 232753, 235699, 243343, 246049, 260339, 261799, 270073, 295363, 295703, 302459, 315199, 331399, 362003, 364079, 373669, 380729, 381793, 385943, 414809
Offset: 1

Views

Author

Labos Elemer, Jan 28 2000

Keywords

Comments

Old name was "Primes p(k) such that p(k+2)-p(k+1)=p(k+1)-p(k)=24."

Examples

			40039 is followed by 40063 and 40087, consecutive primes with equal distance of 24.

Links

Crossrefs

Subsequence of A098974.
Cf. A001223, A033451, A047948, A052188, A052189.

Programs

  • Mathematica
    Select[Partition[Prime[Range[40000]],3,1],Differences[#]=={24,24}&][[All,1]] (* Harvey P. Dale, May 09 2019 *)
  • PARI
    list(lim) = {my(p1 = 2, p2 = 3); forprime(p3 = 5, lim, if(p2 - p1 == 24 && p3 - p2 == 24, print1(p1, ", ")); p1 = p2; p2 = p3);} \\ Amiram Eldar, Feb 28 2025

Extensions

Name changed by Jon E. Schoenfield, May 30 2018

A052197 Primes p such that p, p+36, p+72 are consecutive primes.

Original entry on oeis.org

255767, 704321, 806821, 884501, 913067, 1065137, 1216177, 1448497, 1526191, 1532471, 1640971, 1918571, 2071087, 2275067, 2276431, 2336671, 2347591, 2376721, 2778547, 3098561, 3190601, 3248941, 3259001, 3452107, 3558481
Offset: 1

Views

Author

Labos Elemer, Jan 28 2000

Keywords

Comments

Old name was: Primes p(k) such that p(k+2)-p(k+1)=p(k+1)-p(k)=36.

Examples

			a(3) = 704321 is followed by 704357 and 704393, consecutive primes with equal distance of d = 36.

Links

Crossrefs

Subsequence of A134117.
Cf. A001223, A033451, A047948, A052195.

Programs

  • Mathematica
    Select[Partition[Prime[Range[255000]],3,1],Differences[#]=={36,36}&][[All,1]] (* Harvey P. Dale, Feb 16 2018 *)
  • PARI
    is(n)=nextprime(n+1)==n+36 && nextprime(n+37)==n+72 && isprime(n) \\ Charles R Greathouse IV, Jan 07 2013

Extensions

New name from Charles R Greathouse IV, Jan 07 2013
Previous Showing 31-40 of 52 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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