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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A068232 a(n) is the smallest prime p such that p and the next n-1 primes are all == 1 (mod 12).

Original entry on oeis.org

13, 661, 8317, 12829, 586153, 1081417, 7790917, 7790917, 370861009, 370861009, 370861009, 5637496849, 289391626057, 469257742237, 628337233501, 84424712545429, 155494152002017, 341821313785729
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Feb 22 2002

Keywords

Comments

Dickson's conjecture implies that a(n) exists for all n.

Links

Crossrefs

Cf. A068227, A068228, A068229, A040117, A068231, A068233, A068234, A068235.

Programs

  • Mathematica
    For[i=n=1, True, Null, For[j=0, jHarvey P. Dale, Dec 24 2020 *)
  • PARI
    {i=n=1; while(1,j=0; while(j

Extensions

Edited by Dean Hickerson, Mar 06 2002
a(12)-a(15) from Giovanni Resta, Feb 18 2006
a(16)-a(18) from Giovanni Resta, Aug 04 2013

A068233 a(n) is the smallest prime p such that p and the next n-1 primes are all == 7 (mod 12).

Original entry on oeis.org

7, 199, 199, 32443, 180799, 180799, 4338787, 84885631, 472798219, 1786054267, 6024282871, 64791932287, 592175010019, 6265824724519, 7816088451907, 24660781037467
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Feb 22 2002

Keywords

Comments

Dickson's conjecture implies that a(n) exists for all n.

Links

Crossrefs

Cf. A068227, A068228, A068229, A040117, A068231, A068232, A068234, A068235.

Programs

  • Mathematica
    For[i=n=1, True, Null, For[j=0, j
  • PARI
    {i=n=1; while(1,j=0; while(j

Extensions

Edited by Dean Hickerson, Mar 06 2002
More terms from Giovanni Resta, Feb 18 2006
a(16) from Giovanni Resta, Aug 04 2013

A068234 a(n) is the smallest prime p such that p and the next n-1 primes are all == 5 (mod 12).

Original entry on oeis.org

5, 509, 4397, 42509, 647417, 647417, 1248869, 13175609, 234946997, 1039154933, 7114719473, 32021552837, 32021552837, 1237381737257, 2904797643617, 2904797643617, 2904797643617
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Feb 22 2002

Keywords

Comments

Dickson's conjecture implies that a(n) exists for all n.
a(18) > 4*10^14. - Giovanni Resta, Aug 04 2013

Links

Crossrefs

Cf. A068227, A068228, A068229, A040117, A068231, A068232, A068233, A068235.

Programs

  • Mathematica
    For[i=n=1, True, Null, For[j=0, jHarvey P. Dale, Feb 02 2022 *)
  • PARI
    {i=n=1; while(1,j=0; while(j

Extensions

Edited by Dean Hickerson, Mar 06 2002
More terms from Giovanni Resta, Feb 18 2006

A068235 a(n) is the smallest prime p such that p and the next n-1 primes are all == 11 (mod 12).

Original entry on oeis.org

11, 467, 1499, 16763, 260339, 2003387, 7722419, 20221283, 927161471, 4284484931, 7355362139, 84805717127, 478527373859, 2046207697631, 7302359785151, 21104656617827, 21104656617827
Offset: 1

Views

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Feb 22 2002

Keywords

Comments

Dickson's conjecture implies that a(n) exists for all n.
a(18) > 4*10^14. - Giovanni Resta, Aug 04 2013

Links

Crossrefs

Cf. A068227, A068228, A068229, A040117, A068231, A068232, A068233, A068234.

Programs

  • Mathematica
    For[i=n=1, True, Null, For[j=0, j
  • PARI
    {i=n=1; while(1,j=0; while(j

Extensions

Edited by Dean Hickerson, Mar 06 2002
More terms from Giovanni Resta, Feb 18 2006
a(16)-a(17) from Giovanni Resta, Aug 04 2013

A160591 Indices of primes congruent to 5 modulo 12.

Original entry on oeis.org

3, 7, 10, 13, 16, 24, 26, 30, 33, 35, 40, 45, 51, 55, 57, 60, 62, 66, 71, 77, 79, 87, 89, 97, 98, 102, 104, 108, 113, 116, 119, 123, 126, 135, 137, 139, 140, 142, 148, 152, 158, 160, 162, 165, 170, 176, 178, 184, 186, 194, 196, 199, 201, 206, 209, 212, 218, 220, 223
Offset: 1

Views

Author

M. F. Hasler, May 21 2009

Keywords

Comments

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 02 2021

Examples

			a(1) = 3 since the 3rd prime, A000040(3) = 5, is the first one to be equal to 5 (mod 12).
a(2) = 7 since the 7th prime, A000040(7) = 17, is the second one to be equal to 5 (mod 12).

Links

Crossrefs

A116602 lists the even terms of this sequence, divided by 2.
Cf. A000720, A040117.

Programs

  • Maple
    res:= NULL: p:= 2:
for m from 2 to 1000 do
  p:= nextprime(p);
  if p mod 12 = 5 then res:= res, m fi;
od:
res; # Robert Israel, Dec 26 2016
  • Mathematica
    Select[{#, Prime[#]}& /@ Range[500], Mod[#[[2]], 12] == 5&] [[All, 1]] (* Jean-François Alcover, Mar 23 2019 *)
Select[Range[300],Mod[Prime[#],12]==5&] (* Harvey P. Dale, Mar 18 2023 *)
  • PARI
    for(n=1,999, prime(n)%12==5 & print1(n","))

Formula

a(n) = A000720(A040117(n)).

A038875 Primes p with legendre(3,p) = -1.

Original entry on oeis.org

2, 5, 7, 17, 19, 29, 31, 41, 43, 53, 67, 79, 89, 101, 103, 113, 127, 137, 139, 149, 151, 163, 173, 197, 199, 211, 223, 233, 257, 269, 271, 281, 283, 293, 307, 317, 331, 353, 367, 379, 389, 401, 439, 449, 461, 463, 487, 499, 509, 521, 523, 547, 557, 569, 571, 593
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Apart from the first term, primes p such that 3 is not a square mod p.
Apart from the first term, identical to A003630.

Links

Crossrefs

Cf. A040117, A003630.

Programs

  • Mathematica
    Select[Prime@Range[120], JacobiSymbol[3, #] == -1 &] (* Vincenzo Librandi, Sep 09 2012 *)
  • PARI
    isok(p) = isprime(p) && (kronecker(3, p) == -1); \\ Michel Marcus, Jan 24 2023

Extensions

Edited by D. S. McNeil, R. J. Mathar and N. J. A. Sloane, Aug 15 2010

A167055 Numbers k such that 12*k + 5 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 9, 11, 12, 14, 16, 19, 21, 22, 23, 24, 26, 29, 32, 33, 37, 38, 42, 43, 46, 47, 49, 51, 53, 54, 56, 58, 63, 64, 66, 67, 68, 71, 73, 77, 78, 79, 81, 84, 87, 88, 91, 92, 98, 99, 101, 102, 106, 107, 108, 113, 114, 117, 119, 123, 124, 129, 133, 134, 136, 141
Offset: 1

Views

Author

Michael B. Porter, Oct 27 2009

Keywords

Comments

Corresponds to odd numbers in A024898.

Examples

			2 is in the sequence since 12*2+5 = 29 is prime.

Links

Crossrefs

Cf. A110801, A167056, A167057, A024898, primes are in A040117.

Programs

  • Magma
    [n: n in [1..150] | IsPrime(12*n+5)]; // Vincenzo Librandi, May 20 2014
  • Mathematica
    Select[Range[0,150],PrimeQ[12#+5]&] (* Harvey P. Dale, Oct 07 2012 *)
  • PARI
    isA167055(n) = isprime(12*n+5)

A243183 Primes of the form 2x^2+2xy+5y^2.

Original entry on oeis.org

2, 5, 17, 29, 41, 53, 89, 101, 113, 137, 149, 173, 197, 233, 257, 269, 281, 293, 317, 353, 389, 401, 449, 461, 509, 521, 557, 569, 593, 617, 641, 653, 677, 701, 761, 773, 797, 809, 821, 857, 881, 929, 941, 953, 977, 1013, 1049, 1061, 1097, 1109, 1181, 1193, 1217, 1229, 1277, 1289, 1301, 1361, 1373, 1409, 1433, 1481, 1493, 1553, 1601, 1613, 1637
Offset: 1

Views

Author

N. J. A. Sloane, Jun 02 2014

Keywords

Comments

Because all terms in A243182 are in {0, 2, 5, 6, 8, 9} (mod 12) and 5 is the only one in this set coprime to 12, this is (apart from the 2) a subsequence of A040117. - R. J. Mathar, Jul 07 2023
This sequence is actually equal to A040117, except for the additional initial a(1) = 2 here (and indexing of the remaining terms). - M. F. Hasler, Jul 03 2025

Links

Crossrefs

Primes in A243182.
Cf. A040117 (the same without the initial 2 here).

A116613 Values of n such that prime(2n+1) mod 12 = 5.

Original entry on oeis.org

1, 3, 6, 16, 17, 22, 25, 27, 28, 35, 38, 39, 43, 44, 48, 56, 59, 61, 67, 68, 69, 82, 99, 100, 104, 111, 113, 122, 127, 129, 132, 133, 145, 146, 156, 161, 162, 171, 172, 176, 179, 183, 186, 189, 190, 202, 209, 210, 234, 238, 250, 251, 258, 261, 272, 275, 280, 284
Offset: 1

Views

Author

Roger L. Bagula, Mar 29 2006

Keywords

Examples

			25 is in the sequence because the 51st prime is 233 and 233 mod 12 = 5.

Links

Crossrefs

Cf. A116602, A116610, A116612-A116617, A160591-A160594. - M. F. Hasler, May 22 2009

Programs

  • Maple
    a:=proc(n) if ithprime(2*n+1) mod 12 = 5 then n else fi end: seq(a(n),n=0..300);
  • Mathematica
    Select[Range[0, 500], Mod[Prime[2*# + 1], 12] == 5 &] (* G. C. Greubel, Nov 19 2017 *)
  • PARI
    for(n=1,999, prime(2*n+1)%12==5 & print1(n",")) \\ M. F. Hasler, May 22 2009

Formula

Equals the integer part of { odd terms in A160591 = A000720(A040117) } / 2. - M. F. Hasler, May 22 2009

Extensions

Edited by N. J. A. Sloane, Apr 05 2006

A141682 Number of isomorphism classes of (2n+1)-reflexive polygons.

Original entry on oeis.org

16, 1, 12, 29, 1, 61, 81, 1, 113, 131, 2, 163, 50, 2, 215, 233, 2, 34, 285, 3, 317, 335, 2, 367, 182, 3, 419, 72, 4, 469, 489, 3, 93, 539, 4, 571, 591, 3, 185, 641, 5, 673, 131, 5, 725, 240, 6, 148, 795, 5, 827, 845, 3, 877, 897, 7, 929, 186, 6, 338, 656, 7, 240, 1049, 8, 1081, 393, 5, 1133, 1151, 8, 542, 245, 7, 1235, 1253
Offset: 0

Views

Author

Benjamin Nill, Jul 02 2012

Keywords

Comments

There are no l-reflexive polygons for even index l.

Examples

			a(0)=16 equals the number of isomorphism classes of (1-)reflexive polygons, A090045(2).

Links

Crossrefs

Cf. A090045.

Formula

It seems that for n > 2, a(n) = 17*n - k where k = 21, 22, 23, 24 iff 2*n+1 is a prime from A068228, A068229, A040117, A068231, respectively. - Andrey Zabolotskiy, Apr 21 2022
Previous Showing 11-20 of 28 results. Next

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

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