A153409 -id:A153409 - cp's OEIS frontend

A153410 Middle of 3 consecutive prime numbers, p1, p2, p3, such that p1p2p3d1d2 = average of twin prime pairs; d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

3, 5, 23, 67, 233, 503, 683, 1013, 1759, 2099, 2797, 3169, 10663, 12391, 12899, 13487, 15149, 18583, 20563, 21881, 25373, 26237, 26681, 33613, 36787, 36943, 41411, 41443, 43573, 61547, 63337, 63841, 68909, 71999, 75721, 76367, 76481, 86677

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

nonn

			2*3*5*1*2 = 60 and 60 +- 1 are primes.
3*5*7*2*2 = 420 and 420 +- 1 are primes.
19*23*29*4*6 = 304152 and 304152 +- 1 are primes.

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

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408, A153409.

lst={};Do[p1=Prime[n];p2=Prime[n+1];p3=Prime[n+2];d1=p2-p1;d2=p3-p2;a=p1*p2*p3*d1*d2;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p2]],{n,8!}];lst
cpnQ[{a_,b_,c_}]:=Module[{x=Times@@Join[{a,b,c},Differences[ {a,b,c}]]}, AllTrue[ x+{1,-1},PrimeQ]]; Select[Partition[ Prime[Range[ 10000]],3,1], cpnQ][[All,2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 01 2020 *)

A153411 Larger of 3 consecutive prime numbers such that p1p2p3d1d2=average of twin prime pairs; p1,p2,p3 consecutive prime numbers; d1(delta)=p2-p1, d2(delta)=p3-p2.

Original entry on oeis.org

5, 7, 29, 71, 239, 509, 691, 1019, 1777, 2111, 2801, 3181, 10667, 12401, 12907, 13499, 15161, 18587, 20593, 21893, 25391, 26249, 26683, 33617, 36791, 36947, 41413, 41453, 43577, 61553, 63347, 63853, 68917, 72019, 75731, 76369, 76487, 86689

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

nonn

2*3*5*1*2=60+-1=primes, 3*5*7*2*2=420+-1=primes, 19*23*29*4*6=304152+-1=primes,...

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

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408, A153409, A153410

lst={};Do[p1=Prime[n];p2=Prime[n+1];p3=Prime[n+2];d1=p2-p1;d2=p3-p2;a=p1*p2*p3*d1*d2;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p3]],{n,8!}];lst
tppQ[n_]:=Module[{c=Times@@Join[n,Differences[n]]},AllTrue[c+{1,-1}, PrimeQ]]; Transpose[Select[Partition[Prime[Range[10^4]],3,1], tppQ]] [[3]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 17 2016 *)

A153413 Smaller of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.

Original entry on oeis.org

3, 5, 29, 59, 137, 179, 239, 419, 617, 1049, 1607, 1697, 1787, 2267, 2309, 2729, 3257, 3389, 3527, 3767, 4157, 4217, 4337, 4799, 5639, 5867, 6659, 6689, 6869, 6959, 7487, 7547, 7589, 8537, 8627, 8969, 9629, 9857, 9929, 10457, 11117, 11969, 12539, 13337

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

nonn

3*5+4=19 prime, 5*7+6=41 prime, 29*31+30=929 prime, ...

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408, A153409, A153410

lst={};Do[p1=Prime[n];p2=Prime[n+1];If[p2-p1==2,a=p1*p2+(p1+1);If[PrimeQ[a],AppendTo[lst,p1]]],{n,7!}];lst

A153414 Larger of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.

Original entry on oeis.org

5, 7, 31, 61, 139, 181, 241, 421, 619, 1051, 1609, 1699, 1789, 2269, 2311, 2731, 3259, 3391, 3529, 3769, 4159, 4219, 4339, 4801, 5641, 5869, 6661, 6691, 6871, 6961, 7489, 7549, 7591, 8539, 8629, 8971, 9631, 9859, 9931, 10459, 11119, 11971, 12541, 13339

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

nonn

3*5+4=19 prime, 5*7+6=41 prime, 29*31+30=929 prime, ...

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

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408, A153409, A153410, A153413

lst={};Do[p1=Prime[n];p2=Prime[n+1];If[p2-p1==2,a=p1*p2+(p1+1);If[PrimeQ[a],AppendTo[lst,p2]]],{n,7!}];lst
Transpose[Select[Select[Partition[Prime[Range[1600]],2,1],Last[#]- First[#] == 2&], PrimeQ[Times@@#+Mean[#]]&]][[2]] (* Harvey P. Dale, Jan 23 2012 *)

cp's OEIS Frontend

A153410 Middle of 3 consecutive prime numbers, p1, p2, p3, such that p1p2p3d1d2 = average of twin prime pairs; d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

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A153411 Larger of 3 consecutive prime numbers such that p1p2p3d1d2=average of twin prime pairs; p1,p2,p3 consecutive prime numbers; d1(delta)=p2-p1, d2(delta)=p3-p2.

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A153413 Smaller of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.

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Author

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Programs

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A153414 Larger of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.

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Author

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Mathematica

cp's OEIS Frontend

A153410 Middle of 3 consecutive prime numbers, p1, p2, p3, such that p1*p2*p3*d1*d2 = average of twin prime pairs; d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

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Mathematica

A153411 Larger of 3 consecutive prime numbers such that p1*p2*p3*d1*d2=average of twin prime pairs; p1,p2,p3 consecutive prime numbers; d1(delta)=p2-p1, d2(delta)=p3-p2.

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Mathematica

A153413 Smaller of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A153414 Larger of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A153410 Middle of 3 consecutive prime numbers, p1, p2, p3, such that p1p2p3d1d2 = average of twin prime pairs; d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

A153411 Larger of 3 consecutive prime numbers such that p1p2p3d1d2=average of twin prime pairs; p1,p2,p3 consecutive prime numbers; d1(delta)=p2-p1, d2(delta)=p3-p2.