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.

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 *)

A249798 Numbers k such that the product of the first k primes minus the (k+1)-th prime is prime.

Original entry on oeis.org

3, 4, 5, 6, 8, 22, 23, 24, 35, 73, 83, 147, 553, 1098, 1115, 1542, 2097, 2149, 8712, 19965, 25046, 30987, 38635
Offset: 1

Views

Author

Ivan N. Ianakiev, Nov 06 2014

Keywords

Examples

			p(1)*p(2)*p(3)*p(4) - p(5) = 2*3*5*7 - 11 = 199. 199 is prime, therefore 4 is in the sequence.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[1000],PrimeQ[Times@@(Prime[Range[#]])-Prime[#+1]]&]
  • PARI
    lista(nn) = {prp = 1; for(n=1, nn, prp *= prime(n); if (isprime(prp-prime(n+1)), print1(n, ", ")););} \\ Michel Marcus, Nov 06 2014

Formula

a(n) = primepi(A093078(n)). - Michel Marcus, Nov 06 2014

Extensions

a(17)-a(18) using A093078 from Michael S. Branicky, Mar 18 2024
a(19)-a(23) from Henri Lifchitz, Nov 08 2024

A367182 Primes of the form (k-th primorial) - (k+1)st prime.

Original entry on oeis.org

23, 199, 2297, 30013, 9699667, 3217644767340672907899084554047, 267064515689275851355624017992701, 23768741896345550770650537601358213, 1492182350939279320058875736615841068547583863326864530259
Offset: 1

Views

Author

Daniel D Gibson, Nov 08 2023

Keywords

Comments

Conjecture: sequence is infinite.

Examples

			primorial(4) - prime(4+1) = 2*3*5*7 - prime(5) = 210 - 11 = 199, which is prime, so 199 is a term.
		

Crossrefs

Cf. A002110, A093078, A249798 (corresponding k's).
The prime numbers in A060882.
A038708 with subtraction instead of addition.
Showing 1-3 of 3 results.