A263483 a(n) = prime(n)+(prime(n) modulo 6).

4, 6, 10, 8, 16, 14, 22, 20, 28, 34, 32, 38, 46, 44, 52, 58, 64, 62, 68, 76, 74, 80, 88, 94, 98, 106, 104, 112, 110, 118, 128, 136, 142, 140, 154, 152, 158, 164, 172, 178, 184, 182, 196, 194, 202, 200, 212, 224, 232, 230, 238, 244, 242, 256, 262, 268, 274, 272, 278, 286, 284, 298, 308, 316, 314

Offset: 1

Author

Zak Seidov, Oct 19 2015

Keywords

• nonn

Comments

For n>2, a(n)-a(n+1)=2 iff prime(n) and prime(n+1) are twin primes; e.g., a(3)-a(4)=10-8=2 and prime(3)=5 and prime(4)=7 are twin primes.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A039704.

Programs

Maple

p:= 1:
for n from 1 to 100 do
  p:= nextprime(p);
  A[n]:= p + (p mod 6);
od:
seq(A[n],n=1..100); # Robert Israel, Jul 18 2018

Mathematica

Table[(p=Prime[n])+Mod[p,6],{n,100}]

PARI

a(n) = apply(x->(x + x%6), prime(n)); \\ Michel Marcus, Oct 27 2015

Formula

a(n) = A000040(n) + A039704(n). - Michel Marcus, Oct 27 2015