A155008 -id:A155008 - cp's OEIS frontend

A155009 Primes p such that (p-a)(p+a)-+ap are primes,a=5.

2, 7, 11, 17, 19, 23, 41, 43, 61, 67, 107, 109, 131, 137, 179, 197, 263, 269, 331, 353, 397, 641, 677, 743, 859, 941, 1163, 1171, 1213, 1303, 1319, 1433, 1447, 1453, 1543, 1601, 1783, 2221, 2351, 2371, 2417, 2503, 2657, 2689, 2791, 2797, 2909, 3037, 3301

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 18 2009

nonn

1*12-35=-23, 1*12+35=47; 6*16-55=96-55=41, 6*16-55=96+55=151, ...

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A125272, A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939, A155006, A155007, A155008

lst={};Do[p=Prime[n];If[PrimeQ[(p-5)*(p+5)-5*p]&&PrimeQ[(p-5)*(p+5)+5*p],AppendTo[lst,p]],{n,7!}];lst
Select[Prime[Range[500]],AllTrue[(#-5)(#+5)+{5#,-5#},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 01 2016 *)

A155010 Primes p such that (p-a)(p+a)-+ap and (p-b)(p+b)-+bp are primes, a=2,b=3.

Original entry on oeis.org

7, 37, 587, 28703, 35677, 36857, 99367, 326707, 361687, 578167, 613573, 619007, 656407, 688783, 702203, 713467, 874823, 922027, 940573, 1045763, 1057907, 1244687, 1371157, 1419697, 1555187, 1665767, 1687187, 1687327, 1799453

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 18 2009

nonn

Cf. A125272, A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939, A155006, A155007, A155008, A155009

lst={};Do[p=Prime[n];If[PrimeQ[(p-2)*(p+2)-2*p]&&PrimeQ[(p-2)*(p+2)+2*p]&&PrimeQ[(p-3)*(p+3)-3*p]&&PrimeQ[(p-3)*(p+3)+3*p],AppendTo[lst,p]],{n,9!}];lst
Select[Prime[Range[200000]],AllTrue[Flatten[{(#-2)(#+2)+{2#,-2#},(#-3)(#+3)+ {3#,-3#}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 26 2015 *)

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A155009 Primes p such that (p-a)(p+a)-+ap are primes,a=5.

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A155010 Primes p such that (p-a)(p+a)-+ap and (p-b)(p+b)-+bp are primes, a=2,b=3.

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cp's OEIS Frontend

A155009 Primes p such that (p-a)*(p+a)-+a*p are primes,a=5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A155010 Primes p such that (p-a)*(p+a)-+a*p and (p-b)*(p+b)-+b*p are primes, a=2,b=3.

Views

Author

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Programs

Mathematica

A155009 Primes p such that (p-a)(p+a)-+ap are primes,a=5.

A155010 Primes p such that (p-a)(p+a)-+ap and (p-b)(p+b)-+bp are primes, a=2,b=3.