cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A088416 A088415 indexed by A000040.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 14, 16, 17, 21, 22, 23, 24, 35, 73, 83, 147, 553, 801, 1098, 1115
Offset: 1

Views

Author

Ray Chandler, Oct 05 2003

Keywords

Crossrefs

Formula

a(n) = k such that A088415(n) = A000040(k).
a(n) = A000720(A088415(n)). - Michel Marcus, Aug 06 2021

Extensions

Offset changed to 1 and a(20)-a(23) from Jinyuan Wang, Aug 06 2021

A093078 Primes p = prime(i) such that p(i)# - p(i+1) is prime.

Original entry on oeis.org

5, 7, 11, 13, 19, 79, 83, 89, 149, 367, 431, 853, 4007, 8819, 8969, 12953, 18301, 18869
Offset: 1

Views

Author

Robert G. Wilson v, Oct 25 2003

Keywords

Comments

a(19) > 22013. - J.W.L. (Jan) Eerland, Dec 19 2022
a(19) > 63317. - J.W.L. (Jan) Eerland, Dec 20 2022

Examples

			3 = p(2) is in the sequence because p(2)# + p(3) = 11 is prime.
		

Crossrefs

Programs

  • Mathematica
    Do[p = Product[ Prime[i], {i, 1, n}]; q = Prime[n + 1]; If[ PrimeQ[p - q], Print[ Prime[n]]], {n, 1, 1435}]
    Module[{nn=1120,pr1,pr2,prmrl},pr1=Prime[Range[nn]];pr2=Prime[Range[ 2, nn+1]]; prmrl=FoldList[Times,pr1];Transpose[Select[Thread[{pr1,pr2, prmrl}], PrimeQ[#[[3]]-#[[2]]]&]][[1]]] (* Harvey P. Dale, Dec 07 2015 *)
    n=1;Monitor[Parallelize[While[True,If[PrimeQ[Product[Prime[k],{k,1,n}]-Prime[n + 1]],Print[Prime[n]]];n++];n],n] (* J.W.L. (Jan) Eerland, Dec 19 2022 *)

Extensions

a(16)-a(18) from J.W.L. (Jan) Eerland, Dec 19 2022

A093077 Primes p = prime(i) such that p(i)# + p(i+1) is prime.

Original entry on oeis.org

2, 3, 5, 13, 17, 19, 43, 53, 59, 73, 367, 6143
Offset: 1

Views

Author

Robert G. Wilson v, Oct 25 2003

Keywords

Comments

Prime(A035346(n)) = a(n). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 19 2004

Examples

			3 = p(2) is in the sequence because p(2)# + p(3) = 11 is prime.
		

Crossrefs

Programs

  • Mathematica
    Do[p = Product[ Prime[i], {i, 1, n}]; q = Prime[n + 1]; If[ PrimeQ[p + q], Print[ Prime[n]]], {n, 1, 1435}]
    With[{nn=1000},NextPrime[#,-1]&/@(Select[Thread[{FoldList[ Times,Prime[ Range[nn]]],Prime[Range[ 2,nn+1]]}], PrimeQ[ Total[#]]&][[All,2]])] (* Harvey P. Dale, Oct 07 2018 *)
Showing 1-3 of 3 results.