A118859 Numbers k such that k-1, k+1, 2*k-1, 2*k+1, 3*k-1 and 3*k+1 are primes.
6, 53550, 420420, 422310, 1624350, 2130240, 3399900, 5199810, 5246010, 6549270, 7384440, 7775880, 9516570, 9565710, 10430280, 11845260, 13207950, 14562870, 14619990, 18747960, 20099940, 21596820, 21968100, 24358950, 24610740, 26916120, 28359240, 30838080
Offset: 1
Keywords
Examples
6 is a term because 5, 7, 11, 13, 17, 19 are all prime.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..4000
Crossrefs
Programs
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Mathematica
Select[Range[25*10^6],AllTrue[Flatten[{#+{1,-1},2#+{1,-1},3#+{1,-1}}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 13 2016 *) -
PARI
isok(k) = isprime(k-1) && isprime(k+1) && isprime(2*k-1) && isprime(2*k+1) && isprime(3*k-1) && isprime(3*k+1); \\ Amiram Eldar, Mar 13 2025
Formula
a(n) = 6*A290811(n).
Extensions
Edited by Don Reble, May 16 2006
a(26)-a(28) from Jon E. Schoenfield, Dec 07 2021