A141873 -id:A141873 - cp's OEIS frontend

A144619 a(n) = 19*n + 8.

8, 27, 46, 65, 84, 103, 122, 141, 160, 179, 198, 217, 236, 255, 274, 293, 312, 331, 350, 369, 388, 407, 426, 445, 464, 483, 502, 521, 540, 559, 578, 597, 616, 635, 654, 673, 692, 711, 730, 749, 768, 787, 806, 825, 844, 863, 882, 901, 920, 939, 958, 977, 996

Offset: 0

Vincenzo Librandi, Jan 15 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008601, A141873, A144620.

I:=[8, 27]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]]; // Vincenzo Librandi, May 14 2012

Range[8, 1500, 19] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
CoefficientList[Series[(8+11*x)/(x-1)^2,{x,0,60}],x] (* Vincenzo Librandi, May 14 2012 *)
LinearRecurrence[{2,-1},{8,27},60] (* Harvey P. Dale, Jun 17 2020 *)

From Vincenzo Librandi, May 14 2012: (Start)
G.f.: (11*x+8)/(1-x)^2.
a(n) = 2*a(n-1) - a(n-2). (End)
E.g.f.: exp(x)*(8 + 19*x). - Elmo R. Oliveira, Apr 04 2025

Offset corrected by Jon E. Schoenfield, Jun 17 2010

A144620 Numbers k such that k and 19*k + 8 are both prime.

Original entry on oeis.org

5, 17, 41, 59, 89, 167, 191, 239, 269, 281, 359, 449, 479, 491, 509, 521, 587, 617, 647, 701, 719, 821, 881, 911, 929, 971, 1031, 1181, 1217, 1259, 1289, 1307, 1361, 1367, 1559, 1601, 1697, 1709, 1721, 1787, 1877, 1889, 1907, 1931, 1949, 1997, 2039, 2129

Offset: 1

Vincenzo Librandi, Jan 15 2009

			For n=5, 19*5 + 8 = 103;
for n=269, 19*269 + 8 = 5119.

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

Cf. A141873, A144619.

[p: p in PrimesUpTo(2500)|IsPrime(19*p+8)] // Vincenzo Librandi, Aug 30 2012

a := proc (n) if isprime(n) = true and isprime(19*n+8) = true then n else end if end proc: seq(a(n), n = 1 .. 2300); # Emeric Deutsch, Jan 27 2009

Select[Prime[Range[400]], PrimeQ[#] &&PrimeQ[19#+8] &] (* Vincenzo Librandi, Aug 30 2012 *)

Extended by Emeric Deutsch, Jan 27 2009

A274202 Primes congruent to 31 mod 65.

Original entry on oeis.org

31, 421, 811, 941, 1201, 1721, 2111, 2371, 3541, 3671, 3931, 4451, 5101, 5231, 5881, 6011, 6271, 6661, 6791, 8221, 8741, 9001, 9391, 9521, 9781, 10301, 10691, 11471, 11731, 12251, 12511, 12641, 13291, 13421, 13681, 14071, 14461, 14591, 14851, 15241, 15761

Offset: 1

Vincenzo Librandi, Jun 13 2016

Subsequence of A030430 and A102732.

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

Cf. A000040, A030430, A102732.

Cf. similar sequences of the type primes congruent to k mod 2*k+3: A045392 (k=2), A102732 (k=5), A138629 (k=7), A141873 (k=8), A141914 (k=10), A141935 (k=11), A141989 (k=13), A142018 (k=14), A142086 (k=16), A142126 (k=17), A142216 (k=19), A142269 (k=20), A142373 (k=22), A142433 (k=23), A142555 (k=25), A142619 (k=26), A142755 (k=28), A142827 (k=29), this sequence (k=31), A154621 (k=32), A154624 (k=34), A154628 (k=35).

[p: p in PrimesUpTo(20000) | p mod 65 eq 31];

Select[Prime[Range[2000]], MemberQ[{31}, Mod[#, 65]] &]
Select[Range[31,16000,65],PrimeQ] (* Harvey P. Dale, May 06 2018 *)

cp's OEIS Frontend

A144619 a(n) = 19*n + 8.

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A144620 Numbers k such that k and 19*k + 8 are both prime.

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A274202 Primes congruent to 31 mod 65.

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