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 1-8 of 8 results.

A155139 Primes p such that both p-+3 are not squarefree.

Original entry on oeis.org

47, 53, 101, 239, 347, 353, 487, 547, 647, 653, 683, 719, 853, 947, 953, 1061, 1153, 1213, 1277, 1447, 1453, 1553, 1663, 1669, 1693, 1697, 1747, 1753, 1847, 2053, 2153, 2251, 2347, 2447, 2647, 2659, 2741, 2753, 2887, 2953, 3041, 3253, 3347, 3359, 3433
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

Comments

47-3=44=2^2*11, 47+3=50=2*5^2, ...

Links

Crossrefs

Cf. A153213, A049282.

Programs

  • Mathematica
    <Harvey P. Dale, May 01 2012 *)
  • PARI
    lista(nn) = forprime(p=3, nn, if (! issquarefree(p-3) && ! issquarefree(p+3), print1(p, ", "))); \\ Michel Marcus, Jul 05 2016

A155140 Primes p such that both p-+4 are not squarefree.

Original entry on oeis.org

293, 347, 571, 829, 1021, 1229, 1327, 1373, 1471, 1621, 2111, 2129, 2371, 2531, 2579, 2879, 2887, 3181, 3271, 3929, 4621, 4801, 4909, 5279, 5333, 5521, 5639, 5683, 5827, 6133, 6421, 6521, 6709, 6863, 6871, 7079, 7321, 7529, 7591, 8179, 8221, 8429, 8963
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

Links

Crossrefs

Cf. A153213, A049282, A155139, A155141, A155142.

Programs

  • Mathematica
    <Harvey P. Dale, Jul 17 2024 *)
  • PARI
    lista(nn) = forprime(p=2, nn, if (! issquarefree(p-4) && ! issquarefree(p+4), print1(p, ", "))); \\ Michel Marcus, Jul 05 2016

A155141 Primes p such that both p-+4 are squarefree.

Original entry on oeis.org

2, 3, 7, 11, 17, 19, 37, 43, 47, 61, 73, 83, 89, 97, 101, 107, 109, 127, 137, 163, 181, 191, 197, 199, 223, 227, 233, 251, 263, 269, 277, 281, 307, 313, 317, 331, 349, 353, 389, 397, 431, 433, 439, 443, 449, 457, 461, 467, 487, 523, 541, 547, 557, 569, 577, 587
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

Links

Crossrefs

Cf. A153213, A049282, A155139, A155140, A155142.

Programs

  • Mathematica
    <Harvey P. Dale, Jun 15 2016 *)
  • PARI
    lista(nn) = forprime(p=2, nn, if (issquarefree(p-4) && issquarefree(p+4), print1(p, ", "))); \\ Michel Marcus, Jul 06 2016

A155142 Primes p that belong neither to A155140 nor to A155141.

Original entry on oeis.org

5, 13, 23, 29, 31, 41, 53, 59, 67, 71, 79, 103, 113, 131, 139, 149, 151, 157, 167, 173, 179, 193, 211, 229, 239, 241, 257, 271, 283, 311, 337, 359, 367, 373, 379, 383, 401, 409, 419, 421, 463, 479, 491, 499, 503, 509, 521, 563, 599, 601, 607, 617, 641, 643
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

Links

Crossrefs

Cf. A153213, A049282, A155139, A155140, A155141.

Programs

  • Mathematica
    <

A153215 Primes p such that none of p-2, p-1, p+1, and p+2 is squarefree.

Original entry on oeis.org

727, 1423, 1861, 3719, 6173, 9749, 11321, 13183, 19073, 20873, 23227, 23473, 23827, 26981, 27883, 34351, 35323, 41263, 42677, 44449, 45127, 45523, 47527, 48751, 49727, 52391, 53623, 53849, 68749, 71993, 72559, 78823, 83609, 89227, 92779
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 20 2008

Keywords

Links

Crossrefs

Cf. A049282, A049097, A039787, A075432, A153207, A153208, A153209, A153210, A153213, A153214.

Programs

  • Mathematica
    << NumberTheory`NumberTheoryFunctions` lst={}; Do[p=Prime[n];If[ !SquareFreeQ[p-1]&&!SquareFreeQ[p+1]&&!SquareFreeQ[p-2]&&!SquareFreeQ[p+2],AppendTo[lst,p]],{n,4*7!}]; lst

A155143 Primes p such that p-+2, p-+4, p-+6 are squarefree.

Original entry on oeis.org

17, 37, 89, 107, 109, 197, 199, 233, 307, 397, 433, 449, 467, 487, 557, 593, 613, 647, 683, 701, 757, 809, 811, 883, 953, 991, 1009, 1061, 1063, 1097, 1117, 1151, 1153, 1259, 1297, 1459, 1493, 1511, 1549, 1601, 1637, 1657, 1693, 1747, 1783, 1889, 1997
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

Comments

All terms == 1 or 8 mod 9. - Robert Israel, Jun 19 2016

Links

Crossrefs

Cf. A153213, A049282, A155139, A155140, A155141, A155142

Programs

  • Maple
    filter:= t -> isprime(t) and andmap(numtheory:-issqrfree, [seq(seq(t+s*j, s=[-1,1]),j=[2,4,6])]):
select(filter, [seq(seq(i+j,j=[-1,1]),i=9..1000,9)]); # Robert Israel, Jun 19 2016
  • Mathematica
    Select[Prime@ Range@ 302, Times @@ Boole@ Map[SquareFreeQ, # + (2 Range@ 7 - 8)] == 1 &] (* Michael De Vlieger, Jun 18 2016 *)
Select[Prime[Range[400]],AllTrue[#+{2,4,6,-2,-4,-6},SquareFreeQ]&] (* Harvey P. Dale, Dec 13 2024 *)

A153214 Primes p such that p+-2 and p+-3 are not squarefree.

Original entry on oeis.org

47, 1447, 1847, 3701, 6653, 11273, 14947, 15727, 17053, 18493, 21661, 24923, 26647, 29153, 32789, 33023, 38873, 39323, 42437, 42923, 44053, 47527, 47977, 49853, 52027, 52153, 56747, 56873, 59929, 71147, 74189, 79427, 80953, 99277, 99713
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 20 2008

Keywords

Crossrefs

Cf. A049282, A049097, A039787, A075432, A153207, A153208, A153209, A153210, A153213

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[ !SquareFreeQ[p-2]&&!SquareFreeQ[p+2]&&!SquareFreeQ[p-3]&&!SquareFreeQ[p+3],AppendTo[lst,p]],{n,3*7!}];lst
Select[Prime[Range[10000]],NoneTrue[#+{-3,-2,2,3},SquareFreeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 27 2019 *)

A155145 Primes p such that p-+1, p-+3, p-+5 are not squarefree.

Original entry on oeis.org

5051, 6353, 6961, 7151, 7547, 8951, 13451, 22447, 36847, 49297, 51061, 51647, 52147, 63649, 68891, 81049, 81553, 82651, 91237, 95747, 108089, 110647, 110899, 117239, 117851, 122207, 124753, 125149, 126517, 136247, 148549, 153953, 154747
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

Links

Crossrefs

Cf. A153213, A049282, A155139, A155140, A155141, A155142, A155143

Programs

  • Mathematica
    <Harvey P. Dale, Dec 05 2020 *)
Showing 1-8 of 8 results.

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

Content is available under The OEIS End-User License Agreement.