A074038 -id:A074038 - cp's OEIS frontend

A074039 If (n, n+2) is the k-th twin prime pair then k else 0.

0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Reinhard Zumkeller, Aug 13 2002

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001359, A006512, A049084, A074038.

seq[max_] := Module[{t = Select[Range[max], And @@ PrimeQ[# + {0, 2}] &], v}, v = Table[0, {max}]; v[[t]] = Range[Length[t]]; v]; seq[100] (* Amiram Eldar, Apr 06 2025 *)

A001359(a(n)) = n, A006512(a(n)) = n+2.

A074041 Product of first n single (i.e., non-twin) primes.

Original entry on oeis.org

2, 46, 1702, 79994, 4239682, 284058694, 22440636826, 1862572856558, 165768984233662, 16079591470665214, 1816993836185169182, 230758217195516486114, 30229326452612659680934, 4746004253060187569906638, 773598693248810573894781994

Offset: 1

Reinhard Zumkeller, Aug 13 2002

nonn

a(n) = 5*A002110(A049084(A074038(n)))/A074040(k), where k is the largest number such that A006512(k) < A007510(n).

			The first four single primes are 2, 23, 37 and 47, therefore a(4) = 2*23*37*47 = 79994.

nn=50;tps=Union[Flatten[Select[Partition[Prime[Range[nn]],2,1],Last[#]- First[#] ==2&]]]; ntps=Complement[Prime[Range[nn]],tps];Rest[ FoldList[ Times,1,ntps]]  (* Harvey P. Dale, Mar 31 2011 *)

a(1) = A007510(1) and a(n) = a(n-1)*A007510(n) for n > 1.

More terms from Harvey P. Dale, Mar 31 2011

cp's OEIS Frontend

A074039 If (n, n+2) is the k-th twin prime pair then k else 0.

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