A141559 Primes of form (p(n)-r(n)), where A141468(n)=r(n)=n-th nonprime and p(n)=n-th prime.

2, 2, 3, 7, 7, 19, 29, 43, 43, 47, 71, 83, 101, 113, 193, 197, 229, 241, 271, 283, 293, 311, 311, 347, 383, 439, 457, 463, 491, 491, 499, 523, 587, 619, 643, 683, 733, 797, 827, 827, 857, 863, 919, 991, 1021, 1031, 1091, 1151, 1187, 1289, 1367, 1367, 1549, 1567

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Mohammad Javaheri, Nikolai A. Krylov, Permutations with a distinct divisor property, arXiv:1904.04227 [math.GR], 2019.

Example

If n=1, then p(1)-r(1)=2-0=2=a(1).
If n=2, then p(2)-r(2)=3-1=2=a(2).
If n=3, then p(3)-r(3)=5-4=1 (nonprime).
If n=4, then p(4)-r(4)=7-6=1 (nonprime).
If n=5, then p(5)-r(5)=11-8=3=a(3).
If n=6, then p(6)-r(6)=13-9=4 (composite).
If n=7, then p(7)-r(7)=17-10=7=a(4).
If n=8, then p(8)-r(8)=19-12=7=a(5).
If n=9, then p(9)-r(9)=23-14=9 (composite).
If n=10, then=p(10)-r(10)=29-15=14 (composite).
If n=11, then p(11)-r(11)=31-16=15 (composite).
If n=12, then p(12)-r(12)=37--18=19=a(6).
If n=13, then p(13)-r(13)=41-20=21 (composite).
If n=14, then p(14)-r(14)=43-21=22 (composite).
If n=15, then p(15)-r(15)=47-22=25 (composite).
If n=16, then p(16)-r(16)=53-24=29=a(7), etc.

Mathematica

Block[{nn = 2000, p, r}, p = Prime@ Range@ PrimePi@ nn; r = Complement[Range[0, nn], p]; Select[Array[p[[#]] - r[[#]] &, Min[Length /@ {p, r}]], PrimeQ]] (* Michael De Vlieger, May 21 2019 *)

Crossrefs

Cf. A000040, A141468.

Sequence in context: A376348 A259254 A095017 * A351732 A211395 A160433

Adjacent sequences: A141556 A141557 A141558 * A141560 A141561 A141562

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 14 2008

Extensions

Edited and extended by Ray Chandler, Aug 19 2008

Status

approved