A060271 Difference between smallest prime following and largest prime preceding 2*(n-th prime).
2, 2, 4, 4, 4, 6, 6, 4, 4, 6, 6, 6, 4, 6, 8, 4, 14, 14, 6, 10, 10, 6, 4, 6, 4, 12, 12, 12, 12, 4, 6, 6, 6, 4, 14, 14, 4, 14, 6, 10, 6, 8, 4, 6, 8, 4, 10, 6, 8, 4, 4, 12, 8, 4, 12, 18, 18, 6, 10, 6, 6, 10, 4, 12, 12, 10, 12, 4, 10, 10, 8, 10, 6, 8, 4, 8, 14, 10, 12, 10, 10, 14, 4, 14, 4, 4, 20, 8
Offset: 1
Keywords
Examples
For n = 1: prime(1) = 2, 2*prime(1) = 4 is between 3 and 5, their difference is 2 = a(1). For n = 6: prime(6) = 13, 2*prime(6) = 26 is between 23 and 29 and their difference is 6 = a(6).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Maple
with(numtheory): [seq(nextprime(2*ithprime(j))-prevprime(2*ithprime(j)),j=1...256)];
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Mathematica
dsplp[n_]:=Module[{np=2Prime[n]},NextPrime[np]-NextPrime[np,-1]]; Array[ dsplp,90] (* Harvey P. Dale, Mar 20 2013 *) -
PARI
a(n) = {my(m = 2*prime(n)); nextprime(m+1) - precprime(m-1);} \\ Amiram Eldar, Feb 08 2025
Extensions
Offset changed to 1 and a(1) prepended by Amiram Eldar, Feb 08 2025