A097490
Primes which are two greater than A097489 terms.
Original entry on oeis.org
5, 17, 167, 302946354048717875530381041444257, 17164738545781348456175905084853738838912866540727619406614703260339837793050935010265073947
Offset: 1
a(3) = 167 = (Product_{k=1..3} A001359(k)) + 2 = 3 * 5 * 11 + 2 = A097489(3) + 2. - _Hartmut F. W. Hoft_, Apr 27 2021
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step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p,p+2}}, {}]], p}]
smallerTwin[n_] := First[Transpose[First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]]]
a097489[n_] := Rest[FoldList[Times, 1, smallerTwin[n]]]
a097490[n_] := Select[Map[#+2&, a097489[n]], PrimeQ]
a097490[39] (* Hartmut F. W. Hoft, Apr 27 2021 *)
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fp(n) = p=1;for(x=1,n,p*=twinl(x);if(isprime(p+2),print1(p+2", ")))
twinl(n) = { local(c,x); c=0; x=1; while(c
A097493
Primes which are two greater than A097492 terms.
Original entry on oeis.org
7, 37, 457, 8647, 51315414607
Offset: 1
a(4) = 8647 = (Product_{k=1..4} A006512(k)) + 2 = 5*7*13*19 + 2 = A097492(4) + 2. - _Hartmut F. W. Hoft_, Apr 27 2021
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step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p,p+2}}, {}]], p}]
largerTwin[n_] := Last[Transpose[First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]]]
a097492[n_] := Rest[FoldList[Times, 1, largerTwin[n]]]
a097493[n_] := Select[Map[#+2&, a097492[n]], PrimeQ]
a097493[68] (* Hartmut F. W. Hoft, Apr 27 2021 *)
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fu(n) = p=1;for(x=1,n,p*=twinu(x);if(isprime(p+2),print1(p+2", ")))
twinu(n) = { local(c,x); c=0; x=1; while(c
A343778
Primes which are two greater than A074040 terms.
Original entry on oeis.org
17, 21800053277, 86984485062381462583582279727, 2948338207972508983453357158259221375675126583677039825367935271466652794027
Offset: 1
a(1) = 17 = A074040(1) + 2 = 3*5 + 2.
A344148
Primes which are two greater than A191746 terms.
Original entry on oeis.org
17, 6779, 293617, 2992417, 24101863, 423722581, 625997497, 929306267, 3377032037, 3825265007, 6458885659, 7150892197, 13075407803, 13860035251, 19434399319, 32531231209, 47475445333, 50281049527, 53207636077, 62607479491, 85780812151, 106014038789, 109384656937, 121991823731, 125813698531
Offset: 1
a(1)=17=A191746(1)+2 is the first prime and a(2)=6779=A191746(7)+2 is the second of the form A191746(k)+2; both are twin primes while a(3)=293617 is not.
Showing 1-4 of 4 results.
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