A023208 -id:A023208 - cp's OEIS frontend

A136017 a(n) = 36n^2 - 1.

35, 143, 323, 575, 899, 1295, 1763, 2303, 2915, 3599, 4355, 5183, 6083, 7055, 8099, 9215, 10403, 11663, 12995, 14399, 15875, 17423, 19043, 20735, 22499, 24335, 26243, 28223, 30275, 32399, 34595, 36863, 39203, 41615, 44099, 46655, 49283, 51983

Offset: 1

Artur Jasinski, Dec 10 2007

The least common multiple of 6*n+1 and 6*n-1. - Colin Barker, Feb 11 2017

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
X. Gourdon and P. Sebah, Collection of series for Pi
Eric Weisstein's World of Mathematics, Pell Equation
Edward Everett Withford, Pell Equation
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A088878, A023208, A136016, A061037, A016910.

[36*n^2 - 1: n in [1..50]]; // Vincenzo Librandi, Jul 09 2012

Mathematica
```
Table[36n^2 - 1, {n, 1, 100}]
```

a(n)=36*n^2-1 \\ Jaume Oliver Lafont, Oct 20 2009

O.g.f.: x*(-35-38*x+x^2)/(-1+x)^3 = 1-35/(-1+x)-108/(-1+x)^2-72/(-1+x)^3. - R. J. Mathar, Dec 12 2007
a(n) = A061037(12n+10)=(6n-1)*(6n+1). - Paul Curtz, Sep 25 2008
Sum_{k>=1} (-1)^(k+1)/a(k) = (Pi-3)/6. - Jaume Oliver Lafont, Oct 20 2009
E.g.f.: 1 + (36 x^2 + 26 x - 1) exp(x). - Robert Israel, Jun 09 2016
Product_{n >= 1} A016910(n) / a(n) = Pi / 3. - Fred Daniel Kline, Jun 09 2016
Sum_{n>=1} 1/a(n) = 1/2 - sqrt(3)*Pi/12. - Amiram Eldar, Jun 27 2020

A136088 Son primes of order 11.

Original entry on oeis.org

5, 47, 83, 89, 113, 149, 167, 173, 179, 233, 239, 293, 383, 389, 443, 569, 587, 599, 683, 797, 839, 947, 1013, 1019, 1097, 1103, 1223, 1229, 1259, 1283, 1289, 1373, 1409, 1427, 1439, 1493, 1499, 1523, 1559, 1913, 1997, 2003, 2027, 2039, 2069, 2087, 2099

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136086.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136087, A136089, A136090, A136091.

n = 11; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a

A136089 Son primes of order 12.

Original entry on oeis.org

5, 7, 13, 17, 19, 23, 41, 59, 61, 67, 79, 83, 101, 107, 109, 131, 137, 139, 163, 173, 181, 191, 199, 229, 233, 251, 257, 263, 277, 293, 307, 317, 347, 353, 359, 367, 373, 389, 397, 419, 431, 461, 467, 521, 523, 569, 577, 587, 607, 613, 653, 683, 691, 709, 727

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136087. For son primes of order 11 see A136088.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136087, A136088, A136090, A136091.

n = 12; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a

A136090 Son primes of order 13.

Original entry on oeis.org

3, 23, 29, 31, 43, 59, 73, 83, 101, 109, 139, 149, 193, 199, 223, 233, 251, 263, 293, 311, 331, 359, 379, 389, 401, 409, 421, 433, 443, 449, 461, 463, 479, 499, 541, 563, 571, 601, 641, 643, 653, 739, 769, 773, 821, 823, 829, 839, 853, 863, 881, 911, 991, 1019

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136087. For son primes of order 11 see A136088. For son primes of order 12 see A136088.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136087, A136088, A136089, A136091.

n = 13; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a

A136091 Son primes of order 14.

Original entry on oeis.org

5, 11, 17, 41, 71, 89, 101, 137, 149, 167, 197, 239, 251, 257, 269, 317, 347, 401, 431, 449, 461, 521, 569, 617, 641, 659, 677, 701, 719, 839, 881, 1031, 1049, 1091, 1109, 1277, 1289, 1367, 1427, 1439, 1487, 1499, 1571, 1601, 1637, 1667, 1721, 1847, 1871

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136087. For son primes of order 11 see A136088. For son primes of order 12 see A136089. For son primes of order 13 see A136090.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A023208, A023218, A023225, A023235, A094524, A136019, A136020, A136026, A136027, A023208, A136082, A136083, A136084, A136085, A136086, A136087, A136088, A136089, A136090.

n = 14; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a

A136071 Father primes of order 2.

Original entry on oeis.org

19, 29, 59, 89, 149, 239, 269, 359, 419, 449, 509, 569, 659, 839, 1259, 1289, 1319, 1409, 1559, 1949, 2099, 2309, 2339, 2399, 2459, 2549, 2609, 2789, 2819, 2939, 2969, 2999, 3089, 3209, 3299, 3389, 3719, 3989, 4049, 4139, 4289, 4409, 4649, 4889, 4919

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A023208, A094524, A136019, A136020, A136026, A136027, A136072, A136073, A136074, A136075, A136076, A136077, A136078, A136079, A136080.

n = 2; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136072 Father primes of order 3.

Original entry on oeis.org

41, 83, 97, 139, 167, 223, 293, 307, 419, 433, 503, 587, 727, 769, 797, 1049, 1063, 1217, 1259, 1399, 1483, 1567, 1609, 1637, 1693, 1847, 1889, 1973, 1987, 2477, 2617, 2659, 2687, 2729, 2939, 2953, 3023, 3037, 3079, 3359, 3499, 3527, 3793, 3947, 3989

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

Primes of the form 7p+6 where p is prime. - David Radcliffe, Nov 30 2015

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

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071.

Cf. A023208, A094524, A136019, A136020, A136026, A136027, A136071, A136073, A136074, A136075, A136076, A136077, A136078, A136079, A136080.

select(t -> isprime(t) and isprime((t-6)/7), [seq(i,i=13..10000, 14)]); # Robert Israel, Nov 30 2015

n = 3; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

Typo in Mathematica program fixed by David Radcliffe, Nov 30 2015

A136073 Father primes of order 4.

Original entry on oeis.org

53, 71, 107, 179, 269, 431, 557, 647, 719, 809, 881, 971, 1151, 1187, 1259, 1367, 1511, 1619, 1637, 1907, 2069, 2267, 2447, 2861, 3041, 3581, 3617, 3779, 3797, 4049, 4157, 4211, 4391, 4877, 4931, 5021, 5147, 5399, 5417, 5471, 5939, 6101, 6317, 6389, 6551

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A023208, A094524, A136019, A136020, A136026, A136027, A136071, A136072, A136074, A136075, A136076, A136077, A136078, A136079, A136080.

n = 4; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136074 Father primes of order 5.

Original entry on oeis.org

43, 131, 197, 263, 461, 593, 659, 1187, 1451, 1847, 1913, 1979, 2111, 2837, 2903, 2969, 4289, 4421, 4751, 5081, 5147, 5279, 5741, 6203, 6269, 6599, 7127, 7193, 7457, 7523, 7919, 8513, 9041, 9239, 9437, 9767, 10427, 10691, 11351, 11549, 11681, 12011

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072. For father primes of order 4 see A136073.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A023208, A094524, A136019, A136020, A136026, A136027, A136071, A136072, A136073, A136075, A136076, A136077, A136078, A136079, A136080.

n = 5; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

A136075 Father primes of order 6.

Original entry on oeis.org

103, 181, 233, 311, 389, 571, 701, 883, 1039, 1091, 1429, 1481, 1663, 1949, 2053, 2131, 2339, 2521, 2963, 3041, 3119, 3613, 3691, 3821, 4003, 4133, 4523, 4549, 4679, 4783, 4861, 5641, 5849, 5953, 6343, 6551, 7253, 7331, 7643, 8059, 8423, 8501, 8761

Offset: 1

Artur Jasinski, Dec 12 2007

nonn

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072. For father primes of order 4 see A136073. For father primes of order 5 see A136074.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A023208, A094524, A136019, A136020, A136026, A136027, A136071, A136072, A136073, A136074, A136076, A136077, A136078, A136079, A136080.

n = 6; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a

cp's OEIS Frontend

A136017 a(n) = 36n^2 - 1.

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A136088 Son primes of order 11.

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A136089 Son primes of order 12.

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A136090 Son primes of order 13.

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A136091 Son primes of order 14.

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A136071 Father primes of order 2.

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A136072 Father primes of order 3.

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A136073 Father primes of order 4.

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A136074 Father primes of order 5.

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