A242215 -id:A242215 - cp's OEIS frontend

A163635 a(n) = 3*A022004(n) + 8.

23, 41, 59, 131, 311, 329, 581, 689, 941, 1049, 1391, 1931, 2471, 2579, 2651, 3281, 3839, 3911, 4289, 4451, 4469, 4829, 5621, 5999, 6251, 6719, 6809, 7979, 8069, 9761, 10391, 10589, 11021, 11759, 12011, 12389, 13559, 13919, 14369, 14801

Offset: 1

Vincenzo Librandi, Aug 02 2009

Sum of the members of the n-th prime triple (p, p+2, p+6).

All terms are congruent to 5 (mod 18). See A242215. - Robert Bilinski, Sep 24 2019

			23 is in the sequence because 23 = 5+7+11 = 3*5+8.
41 is in the sequence because 41 = 11+13+17 = 3*11+8.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A022004, A073648, A098412.

Cf. A242215.

[(3*p+8): p in PrimesUpTo(1000)| IsPrime(p+6) and IsPrime(p+2)]; // Vincenzo Librandi, Jan 06 2018

8 + 3*Select[Prime[Range[1000]], PrimeQ[# + 2] && PrimeQ[# + 6] &] (* Vincenzo Librandi, Jan 04 2014 *)

is(n)=n%18==5 && isprime(n\3-2) && isprime(n\3) && isprime(n\3+4) \\ Charles R Greathouse IV, Jan 06 2018

a(n) = A022004(n) + (A022004(n)+2) + (A022004(n)+6);

a(n) = A022004(n) + A073648(n) + A098412(n).

Notation normalized by R. J. Mathar, Aug 07 2009

A350521 a(n) = 18*n + 4.

Original entry on oeis.org

4, 22, 40, 58, 76, 94, 112, 130, 148, 166, 184, 202, 220, 238, 256, 274, 292, 310, 328, 346, 364, 382, 400, 418, 436, 454, 472, 490, 508, 526, 544, 562, 580, 598, 616, 634, 652, 670, 688, 706, 724, 742, 760, 778, 796, 814, 832, 850, 868, 886, 904, 922, 940, 958

Offset: 0

Omar E. Pol, Jan 03 2022

Second column of A006370 (the Collatz or 3x+1 map) when it is interpreted as a rectangular array with six columns read by rows.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Bisection of A017209.

Cf. A006370, A008600, A016921, A017185, A242215, A298035.

GAP
```
List([0..53], n-> 18*n+4)
```
Magma
```
[18*n+4: n in [0..53]];
```
Maple
```
seq(18*n+4, n=0..53);
```
Mathematica
```
Table[18n+4, {n, 0, 53}]
```
Maxima
```
makelist(18*n+4, n, 0, 53);
```
PARI
```
a(n)=18*n+4
```
Python
```
[18*n+4 for n in range(53)]
```

a(n) = A242215(n) - 1.
a(n) = A298035(n+1) + 1.
From Elmo R. Oliveira, Apr 08 2024: (Start)
G.f.: 2*(2+7*x)/(1-x)^2.
E.g.f.: 2*exp(x)*(2 + 9*x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2.
a(n) = 2*A017185(n) = A006370(A016921(n)). (End)

cp's OEIS Frontend

A163635 a(n) = 3*A022004(n) + 8.

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