A153405 -id:A153405 - cp's OEIS frontend

A153406 Smallest of 3 consecutive prime numbers such that p1p2p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

4813, 9007, 13831, 33791, 35023, 48337, 51577, 52153, 61297, 62207, 77743, 95107, 102607, 105137, 105673, 109663, 111767, 114781, 119747, 128221, 135367, 136727, 138679, 149197, 153949, 159787, 163199, 165437, 174829, 188677, 195973, 208009

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

nonn

4813*4817*4831+4+14=112002971670+-1=primes,...

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

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404, A153405

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+1;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p1]],{n,8!}];lst
s3cpnQ[n_]:=Module[{c=Times@@n+Total[Differences[n]]+1},AllTrue[c+{1,-1}, PrimeQ]]; Transpose[Select[Partition[ Prime[Range[ 20000]],3,1], s3cpnQ]] [[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 05 2014 *)

A153407 Middle of 3 consecutive prime numbers such that p1p2p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

Original entry on oeis.org

4817, 9011, 13841, 33797, 35027, 48341, 51581, 52163, 61331, 62213, 77747, 95111, 102611, 105143, 105683, 109673, 111773, 114797, 119759, 128237, 135389, 136733, 138683, 149213, 153953, 159791, 163211, 165443, 174851, 188681, 195977, 208037

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

nonn

4813*4817*4831+4+14=112002971670+-1=primes,...

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

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404, A153405, A153406

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+1;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p2]],{n,8!}];lst
cnpQ[{a_,b_,c_}]:=Module[{p=a*b*c+(b-a)+(c-b)+1},And@@PrimeQ[p+{1,-1}]]; Transpose[Select[Partition[Prime[Range[20000]],3,1],cpnQ]][[2]] (* Harvey P. Dale, Jul 30 2013 *)

A153408 Largest of 3 consecutive prime numbers such that p1p2p3 + d1 + d2 + 1 = average of twin prime pairs, d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

Original entry on oeis.org

4831, 9013, 13859, 33809, 35051, 48353, 51593, 52177, 61333, 62219, 77761, 95131, 102643, 105167, 105691, 109717, 111779, 114799, 119771, 128239, 135391, 136739, 138727, 149239, 153991, 159793, 163223, 165449, 174859, 188687, 195991, 208049

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

nonn

			4813*4817*4831 + 4 + 14 = 112002971670 and 112002971670 +- 1 are primes.

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

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404, A153405, A153406, A153407.

[NthPrime(k+2):k in [1..20000]| IsPrime(q-1) and IsPrime(q+1) where q is NthPrime(k)* NthPrime(k+1)* NthPrime(k+2)+ NthPrime(k+2)- NthPrime(k)+1]; // Marius A. Burtea, Dec 22 2019

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+1;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p3]],{n,8!}];lst
Select[Partition[Prime[Range[20000]],3,1],AllTrue[Times@@#+Total[ Differences[ #]]+ {2,0},PrimeQ]&][[All,3]] (* Harvey P. Dale, Apr 22 2022 *)

Definition modified by Harvey P. Dale, Apr 22 2022

cp's OEIS Frontend

A153406 Smallest of 3 consecutive prime numbers such that p1p2p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A153407 Middle of 3 consecutive prime numbers such that p1p2p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A153408 Largest of 3 consecutive prime numbers such that p1p2p3 + d1 + d2 + 1 = average of twin prime pairs, d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Extensions

cp's OEIS Frontend

A153406 Smallest of 3 consecutive prime numbers such that p1*p2*p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A153407 Middle of 3 consecutive prime numbers such that p1*p2*p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A153408 Largest of 3 consecutive prime numbers such that p1*p2*p3 + d1 + d2 + 1 = average of twin prime pairs, d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Extensions

A153406 Smallest of 3 consecutive prime numbers such that p1p2p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

A153407 Middle of 3 consecutive prime numbers such that p1p2p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

A153408 Largest of 3 consecutive prime numbers such that p1p2p3 + d1 + d2 + 1 = average of twin prime pairs, d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.