A048598 -id:A048598 - cp's OEIS frontend

A048599 Partial products of the sequence (A001097) of twin primes.

1, 3, 15, 105, 1155, 15015, 255255, 4849845, 140645505, 4360010655, 178760436855, 7686698784765, 453515228301135, 27664428926369235, 1964174453772215685, 143384735125371745005, 14481858247662546245505

Offset: 0

Den Roussel (DenRoussel(AT)webtv.net)

			a(0) = 1 by the usual convention for an empty product. - _N. J. A. Sloane_, Feb 15 2024
a(5) = 15015 because 3 * 5 * 7 * 11 * 13 = 15015.

Cf. A048598, A001097.

nextTwin[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p-2]||PrimeQ[p+2], {p}, {}]], p}]
a001097[n_] := First[NestWhile[nextTwin, {{3}, 3}, Length[First[nextTwin[#]]]<=n&]]
a048599[n_] := FoldList[Times, 1, a001097[n]]
a048599[16] (* Hartmut F. W. Hoft, Apr 27 2021 *)
Join[{1},FoldList[Times,Union[Flatten[Select[Partition[Prime[Range[30]],2,1],#[[2]]-#[[1]]==2&]]]]] (* Harvey P. Dale, Feb 15 2024 *)

More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

A153478 Sum of first n isolated (or single) primes A007510.

Original entry on oeis.org

2, 25, 62, 109, 162, 229, 308, 391, 480, 577, 690, 817, 948, 1105, 1268, 1435, 1608, 1819, 2042, 2275, 2526, 2783, 3046, 3323, 3616, 3923, 4240, 4571, 4908, 5261, 5620, 5987, 6360, 6739, 7122, 7511, 7908, 8309, 8718, 9157, 9600

Offset: 1

Omar E. Pol, Dec 27 2008

G. C. Greubel, Table of n, a(n) for n = 1..1000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos

Cf. A000040, A007504, A007510, A048598, A071148, A153474.

Accumulate[Select[Prime[Range[100]],!PrimeQ[#-2]&&!PrimeQ[#+2]&]]  (* Harvey P. Dale, Feb 08 2011 *)

A376890 Alternating sum of twin primes (A001097).

Original entry on oeis.org

3, -2, 5, -6, 7, -10, 9, -20, 11, -30, 13, -46, 15, -56, 17, -84, 19, -88, 21, -116, 23, -126, 25, -154, 27, -164, 29, -168, 31, -196, 33, -206, 35, -234, 37, -244, 39, -272, 41, -306, 43, -376, 45, -386, 47, -414, 49, -472, 51, -518, 53, -546, 55, -562, 57, -584, 59, -600, 61, -748

Offset: 1

Ilya Gutkovskiy, Oct 08 2024

sign

Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes.

Cf. A001097, A008347, A048598.

T1:= select(t -> isprime(t) and isprime(t+2), [seq(i,i=5..1000,6)]):
T:= map(t -> (-t, t+2), T1): T:= [3,op(T)]:
ListTools:-PartialSums(T); # Robert Israel, Nov 08 2024

a(n) = Sum_{k=1..n} (-1)^(k+1) * A001097(k).

a(2*n-1) = 2*n+1.

cp's OEIS Frontend

A048599 Partial products of the sequence (A001097) of twin primes.

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A153478 Sum of first n isolated (or single) primes A007510.

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A376890 Alternating sum of twin primes (A001097).

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