A128659 -id:A128659 - cp's OEIS frontend

A128657 Numbers k such that p(k+1)# - p(k)# - 1 is prime where p(i)# = product of first i primes = A002110(i).

1, 2, 3, 4, 8, 24, 35, 56, 79, 132, 281, 342, 631, 1350, 4929, 5952, 8128

Offset: 1

Pierre CAMI, Mar 19 2007

Cf. A002110, A128420, A128421, A128658, A128659, A128660, A128661, A128662.

isok(n) = {my(pp=prod(k=1, n, prime(k))); isprime(pp*prime(n+1) - pp -1);} \\ Michel Marcus, Sep 20 2019

a(17) from Michael S. Branicky, Oct 06 2024

A128658 Numbers k such that p(k+1)# - p(k)# + 1 is prime where p(i)# = product of first i primes = A002110(i).

Original entry on oeis.org

1, 3, 7, 14, 80, 224, 280, 287, 652, 1509, 2952, 3915, 7771

Offset: 1

Pierre CAMI, Mar 19 2007

Cf. A002110, A128420, A128421, A128657, A128659, A128660, A128661, A128662.

isok(n) = {my(pp=prod(k=1, n, prime(k))); isprime(pp*prime(n+1) - pp + 1);} \\ Michel Marcus, Sep 20 2019

a(13) from Michael S. Branicky, Oct 06 2024

A128660 Numbers n such that p(n+1)#-p(n)#-p(n-1)#+1 is prime where p(i)#=product of first i primes=A002110(i).

Original entry on oeis.org

2, 6, 14, 15, 23, 31, 97, 144, 983, 2587, 3163, 6689

Offset: 1

Pierre CAMI, Mar 19 2007

nonn

Cf. A002110, A128420, A128421, A128657, A128658, A128659, A128661, A128662.

Flatten[Position[#[[3]]-#[[2]]-#[[1]]+1&/@Partition[FoldList[Times,1,Prime[ Range[ 6700]]] ,3,1],?PrimeQ]] (* _Harvey P. Dale, Jul 25 2013 *)

A128661 Numbers k such that p(k+1)# + p(k)# - p(k-1)# - 1 is prime where p(i)# = product of first i primes = A002110(i).

Original entry on oeis.org

3, 7, 14, 15, 21, 32, 34, 47, 67, 69, 174, 369, 568, 3193, 3882, 5426

Offset: 1

Pierre CAMI, Mar 19 2007

Cf. A002110, A128420, A128421, A128657, A128658, A128659, A128660, A128662.

Flatten[Position[Partition[Rest[FoldList[Times,1,Prime[Range[ 600]]]],3,1], ?(PrimeQ[#[[3]]+#[[2]]-#[[1]]-1]&),{1},Heads-> False]]+1 (* _Harvey P. Dale, May 26 2013 *)

a(14)-a(16) from Michael S. Branicky, Jul 22 2023

A128662 Numbers k such that p(k+1)# + p(k)# - p(k-1)# + 1 is prime where p(i)# = product of first i primes = A002110(i).

Original entry on oeis.org

8, 13, 14, 15, 30, 41, 71, 85, 97, 132, 221, 282, 424, 509, 1346, 1348, 3684, 8224

Offset: 1

Pierre CAMI, Mar 19 2007

Cf. A002110, A128420, A128421, A128657, A128658, A128659, A128660, A128661.

Flatten[Position[Partition[FoldList[Times,Prime[Range[1350]]],3,1],?(PrimeQ[ #[[2]]+#[[3]]-#[[1]]+1]&),1,Heads->False]]+1 (* _Harvey P. Dale, May 30 2018 *)

P(n) = factorback(primes(n)); \\ A002110
isok(k) = ispseudoprime(P(k+1)+P(k)-P(k-1)+1); \\ Michel Marcus, Sep 11 2022

a(17) from Michael S. Branicky, Jun 23 2023

a(11) corrected and a(18) from Michael S. Branicky, Dec 11 2024

cp's OEIS Frontend

A128657 Numbers k such that p(k+1)# - p(k)# - 1 is prime where p(i)# = product of first i primes = A002110(i).

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A128658 Numbers k such that p(k+1)# - p(k)# + 1 is prime where p(i)# = product of first i primes = A002110(i).

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A128660 Numbers n such that p(n+1)#-p(n)#-p(n-1)#+1 is prime where p(i)#=product of first i primes=A002110(i).

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A128661 Numbers k such that p(k+1)# + p(k)# - p(k-1)# - 1 is prime where p(i)# = product of first i primes = A002110(i).

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A128662 Numbers k such that p(k+1)# + p(k)# - p(k-1)# + 1 is prime where p(i)# = product of first i primes = A002110(i).

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PARI

Extensions