Search: a155141 -id:a155141
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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
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1,1
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LINKS
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MATHEMATICA
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<<NumberTheory`NumberTheoryFunctions` lst={}; Do[p=Prime[n]; If[SquareFreeQ[p-4]&&SquareFreeQ[p+4], NULL, If[ !SquareFreeQ[p-4]&&!SquareFreeQ[p+4], NULL, AppendTo[lst, p]]], {n, 6!}]; lst
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A155140
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Primes p such that both p-+4 are not squarefree.
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+10
5
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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
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MATHEMATICA
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<<NumberTheory`NumberTheoryFunctions` lst={}; Do[p=Prime[n]; If[ !SquareFreeQ[p-4]&&!SquareFreeQ[p+4], AppendTo[lst, p]], {n, 7!}]; lst
Select[Prime[Range[1200]], NoneTrue[#+{4, -4}, SquareFreeQ]&] (* Harvey P. Dale, Jul 17 2024 *)
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PROG
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(PARI) lista(nn) = forprime(p=2, nn, if (! issquarefree(p-4) && ! issquarefree(p+4), print1(p, ", "))); \\ Michel Marcus, Jul 05 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A155143
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Primes p such that p-+2, p-+4, p-+6 are squarefree.
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+10
2
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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
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COMMENTS
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LINKS
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MAPLE
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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
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MATHEMATICA
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Select[Prime@ Range@ 302, Times @@ Boole@ Map[SquareFreeQ, # + (2 Range@ 7 - 8)] == 1 &] (* Michael De Vlieger, Jun 18 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A155145
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Primes p such that p-+1, p-+3, p-+5 are not squarefree.
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+10
1
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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
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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<<NumberTheory`NumberTheoryFunctions` lst={}; Do[p=Prime[n]; If[ !SquareFreeQ[p-1]&&!SquareFreeQ[p+1]&&!SquareFreeQ[p-3]&&!SquareFreeQ[p+3]&&!SquareFreeQ[p-5]&&!SquareFreeQ[p+5], AppendTo[lst, p]], {n, 3*7!}]; lst
Select[Prime[Range[15000]], NoneTrue[#+{1, 3, 5, -1, -3, -5}, SquareFreeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 05 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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