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 1-6 of 6 results.

A028883 Primes of the form k^2 - 7.

Original entry on oeis.org

2, 29, 137, 317, 569, 1289, 2297, 2909, 3593, 4349, 8093, 9209, 11657, 17417, 19037, 24329, 26237, 30269, 34589, 36857, 41609, 46649, 49277, 51977, 57593, 60509, 72893, 93629, 101117, 108893, 129593, 133949, 147449, 152093, 166457, 191837, 202493, 219017, 224669
Offset: 1

Views

Author

Patrick De Geest

Keywords

Comments

Subsequence of primes of A028881. - Michel Marcus, Apr 11 2015

Links

Crossrefs

Cf. A028881, A028882.

Programs

  • Magma
    [a: n in [3..500] | IsPrime(a) where a is n^2-7]; // Vincenzo Librandi, Dec 01 2011
  • Maple
    A028883:=n->`if`(isprime(n^2-7), n^2-7, NULL): seq(A028883(n), n=1..500); # Wesley Ivan Hurt, Apr 11 2015
  • Mathematica
    Select[Range[3, 410]^2 - 7, PrimeQ] (* Harvey P. Dale, Sep 20 2011 *)
  • PARI
    lista(nn) = forprime (n=1, nn, if (issquare(n+7), print1(n, ", "))) \\ Michel Marcus, Apr 11 2015

Formula

a(n) = A028881(A028882(n)). - Elmo R. Oliveira, Apr 22 2025

Extensions

More terms from Michel Marcus, Apr 11 2015

A296507 Numbers m such that m^2 - 13 is a prime.

Original entry on oeis.org

4, 6, 12, 18, 24, 30, 36, 54, 72, 84, 90, 96, 102, 114, 120, 138, 168, 186, 198, 204, 210, 216, 228, 240, 276, 294, 318, 330, 354, 360, 372, 378, 402, 414, 438, 444, 456, 480, 498, 504, 588, 600, 612, 618, 630, 636, 666, 678, 690, 714, 720, 726, 732, 738, 762
Offset: 1

Views

Author

Zak Seidov, Dec 13 2017

Keywords

Comments

All terms except 4 are divisible by 6. - Robert Israel, Dec 13 2017

Links

Crossrefs

Cf. A028870, A028873, A028876, A028882, A090696.

Programs

  • Maple
    select(n -> isprime(n^2-13), 2*[$2..10^4]); # Robert Israel, Dec 13 2017
  • Mathematica
    Reap[m=4;Do[If[PrimeQ[m^2-13],Sow[m]];m=m+2,{1000}]][[2,1]]
Select[Range[800],PrimeQ[#^2-13]&] (* Harvey P. Dale, Mar 06 2023 *)
  • PARI
    isok(n) = isprime(n^2-13); \\ Michel Marcus, Dec 14 2017

A157183 Primes in A028883, p=m^2-7, such that following prime is m^2+1.

Original entry on oeis.org

2909, 4349, 8093, 24329, 57593, 72893, 93629, 224669, 324893, 331769, 404489, 562493, 608393, 1166393, 1742393, 1822493, 4137149, 4639709, 5788829, 7289993, 7617593, 10265609, 10497593, 10929629, 12110393, 12362249, 14107529, 14243069
Offset: 1

Views

Author

M. F. Hasler, Mar 14 2009

Keywords

Comments

A subset of { A028883(n) | A028882(n) is in A005574 }.

Programs

  • PARI
    forstep( m=4,10^4,2, ispseudoprime( m^2-7 )||next; ispseudoprime( m^2+1 )||next; nextprime(m^2-5)==(m^2+1) & print1(m^2-7,","))

A157934 Numbers m such that m^2+1 is prime and m^2-7 = prevprime(m^2) (= A007917(m^2)).

Original entry on oeis.org

54, 66, 90, 156, 240, 270, 306, 474, 570, 576, 636, 750, 780, 1080, 1320, 1350, 2034, 2154, 2406, 2700, 2760, 3204, 3240, 3306, 3480, 3516, 3756, 3774, 3984, 4056, 4086, 4140, 4146, 4176, 4716, 4734, 4794, 5154, 5370, 5424, 5550, 5664, 5700, 5850, 5856
Offset: 1

Views

Author

M. F. Hasler, Mar 18 2009

Keywords

Comments

The corresponding primes are listed in A157183 resp. A157935.

Links

Crossrefs

Cf. A157183, A028883, A028882, A005574, A157935.

Programs

  • Mathematica
    Select[Range[6000],PrimeQ[#^2+1]&&#^2-7==NextPrime[#^2,-1]&] (* Harvey P. Dale, Mar 19 2020 *)
  • PARI
    forstep(m=2,9999,2, isprime(m^2+1) & precprime(m^2)==m^2-7 & print1(m,","))

A157935 Primes of the form m^2+1 such that m^2-7 = prevprime(m^2) (= A007917(m^2)).

Original entry on oeis.org

2917, 4357, 8101, 24337, 57601, 72901, 93637, 224677, 324901, 331777, 404497, 562501, 608401, 1166401, 1742401, 1822501, 4137157, 4639717, 5788837, 7290001, 7617601, 10265617, 10497601, 10929637, 12110401, 12362257, 14107537, 14243077
Offset: 1

Views

Author

M. F. Hasler, Mar 18 2009

Keywords

Comments

A subsequence of A005574. The values for m are listed in A157934, the next lower prime in A157183.

Links

Crossrefs

Cf. A157183, A028883, A028882, A005574, A001912, A157934.

Programs

  • Mathematica
    Select[Range[4000]^2+1,PrimeQ[#]&&NextPrime[#,-1]==#-8&] (* Harvey P. Dale, Jun 14 2020 *)
  • PARI
    forstep(m=2,9999,2, isprime(m^2+1) & precprime(m^2)==m^2-7 & print1(m^2+1,","))

Formula

a(n) = A157934(n)^2+1 = A157183(n)+8

A309726 Numbers k such that k^2 - 12 is prime.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 25, 29, 35, 41, 49, 53, 59, 61, 79, 85, 91, 95, 97, 103, 107, 113, 119, 121, 137, 139, 145, 149, 163, 169, 173, 179, 181, 185, 191, 205, 209, 227, 233, 235, 245, 251
Offset: 1

Views

Author

Daniel Starodubtsev, Aug 14 2019

Keywords

Comments

All terms are odd and not divisible by 3.

Examples

			11 is in the sequence because 11^2 - 12 = 109, which is prime.

Links

Crossrefs

Cf. A028870, A028873, A028876, A028879, A028882, A028885, A186815, A090696, A296507.
Cf. A056927.

Programs

  • Mathematica
    Select[Range[5,301,2],PrimeQ[#^2-12]&] (* Harvey P. Dale, Dec 23 2019 *)
  • PARI
    select(n->isprime(n^2-12), [1..1000]) \\ Andrew Howroyd, Aug 14 2019

Formula

If A056927(k) = 12, then k is a term. - A.H.M. Smeets, Aug 15 2019
Showing 1-6 of 6 results.

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