A141881 -id:A141881 - cp's OEIS frontend

A124826 Primes congruent to 1 mod 21.

43, 127, 211, 337, 379, 421, 463, 547, 631, 673, 757, 883, 967, 1009, 1051, 1093, 1303, 1429, 1471, 1597, 1723, 1933, 2017, 2143, 2269, 2311, 2437, 2521, 2647, 2689, 2731, 2857, 3067, 3109, 3319, 3361, 3529, 3571, 3613, 3697, 3739, 3823, 3907, 4159, 4201

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A141881.

[p: p in PrimesUpTo(5000) | p mod 21 eq 1 ]; // Vincenzo Librandi, Aug 14 2012

Select[Range[1,5000,21],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2011*)

is(n)=isprime(n) && n%21==1 \\ Charles R Greathouse IV, Jul 01 2016

A141882 Primes congruent to 7 mod 20.

Original entry on oeis.org

7, 47, 67, 107, 127, 167, 227, 307, 347, 367, 467, 487, 547, 587, 607, 647, 727, 787, 827, 887, 907, 947, 967, 1087, 1187, 1307, 1327, 1367, 1427, 1447, 1487, 1567, 1607, 1627, 1667, 1747, 1787, 1847, 1867, 1907, 1987, 2027, 2087, 2207, 2267, 2287, 2347, 2447

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A105854, A141881, A141883.

[p: p in PrimesUpTo(3000) | p mod 20 eq 7 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[7,5000,20],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)
Select[Prime[Range[400]],Mod[#,20]==7&] (* Harvey P. Dale, Jan 08 2023 *)

is(n)=isprime(n) && n%20==7 \\ Charles R Greathouse IV, Jul 01 2016

A141883 Primes congruent to 9 mod 20.

Original entry on oeis.org

29, 89, 109, 149, 229, 269, 349, 389, 409, 449, 509, 569, 709, 769, 809, 829, 929, 1009, 1049, 1069, 1109, 1129, 1229, 1249, 1289, 1409, 1429, 1489, 1549, 1609, 1669, 1709, 1789, 1889, 1949, 2029, 2069, 2089, 2129, 2269, 2309, 2389, 2549, 2609, 2689, 2729

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A105854, A141881, A141882.

[p: p in PrimesUpTo(3000) | p mod 20 eq 9 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[9,5000,20],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)

is(n)=isprime(n) && n%20==9 \\ Charles R Greathouse IV, Jul 01 2016

A122072 Greatest prime less than 10n.

Original entry on oeis.org

7, 19, 29, 37, 47, 59, 67, 79, 89, 97, 109, 113, 127, 139, 149, 157, 167, 179, 181, 199, 199, 211, 229, 239, 241, 257, 269, 277, 283, 293, 307, 317, 317, 337, 349, 359, 367, 379, 389, 397, 409, 419, 421, 439, 449, 457, 467, 479, 487, 499, 509, 509, 523, 523

Offset: 1

Zak Seidov, Oct 16 2006

First repeating terms are 199, 317, 509, 523, 619, 839, 887, 1069, 1129, 1129, 1259, 1327, 1327, 1327, 1409, 1459, 1499, 1637, 1669, 1669, 1709, 1759, 1789, 1847, 1889, 1913, 1951.

a(n) is also the greatest prime factor among composites (A002808) below 20n. For primes of the form 20n + 1, see A141881. - Lekraj Beedassy, Jan 23 2012

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Table[Prime[PrimePi[10 n]], {n, 54}] (* Jayanta Basu, May 24 2013 *)

a(n)=precprime(10*n) \\ Charles R Greathouse IV, Feb 26 2012

A140444 Primes congruent to 1 (mod 14).

Original entry on oeis.org

29, 43, 71, 113, 127, 197, 211, 239, 281, 337, 379, 421, 449, 463, 491, 547, 617, 631, 659, 673, 701, 743, 757, 827, 883, 911, 953, 967, 1009, 1051, 1093, 1163, 1289, 1303, 1373, 1429, 1471, 1499, 1583, 1597, 1667, 1709, 1723, 1877, 1933, 2003, 2017, 2087

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2008

From Federico Provvedi, May 24 2018: (Start)
Also primes congruent to 1 (mod 7).
For every prime p > 2, primes congruent to 1 (mod p) are also congruent to 1 (mod 2*p).
Conjecture: The monic polynomial P(x) = (x+1)^7/x - 1/x = ((x+1)^7-1)/x is irreducible but factorizable over Galois field (mod a(n)) with exactly 6 distinct irreducible factors of degree 1. Examples:
P(x) == (5 + x) (6 + x) (7 + x) (10 + x) (14 + x) (23 + x)    (mod 29)
P(x) == (3 + x) (9 + x) (23 + x) (28 + x) (33 + x) (40 + x)   (mod 43)
P(x) == (24 + x) (27 + x) (35 + x) (40 + x) (42 + x) (52 + x) (mod 71)
P(x) == (5 + x) (8 + x) (65 + x) (84 + x) (86 + x) (98 + x)   (mod 113)
... (End).
Primes in A131877. - Eric Chen, Jun 14 2018

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 526.

Cf. A045437, A045458, A045471, A045473.
A090613 gives prime index.
Cf. A090614.
Cf. A131877.
Primes congruent to 1 (mod k): A000040 (k=1), A065091 (k=2), A002476 (k=3 and 6), A002144 (k=4), A030430 (k=5 and 10), this sequence (k=7 and 14), A007519 (k=8), A061237 (k=9 and 18), A141849 (k=11 and 22), A068228 (k=12), A268753 (k=13 and 26), A132230 (k=15 and 30), A094407 (k=16), A129484 (k=17 and 34), A141868 (k=19 and 38), A141881 (k=20), A124826 (k=21 and 42), A212374 (k=23 and 46), A107008 (k=24), A141927 (k=25 and 50), A141948 (k=27 and 54), A093359 (k=28), A141977 (k=29 and 58), A142005 (k=31 and 62), A133870 (k=32).

Filtered(Filtered([1..2300],n->n mod 14=1),IsPrime); # Muniru A Asiru, Jun 27 2018

[p: p in PrimesUpTo(3000)|p mod 14 in {1}]; // Vincenzo Librandi, Dec 18 2010

select(isprime,select(n->modp(n,14)=1,[$1..2300])); # Muniru A Asiru, Jun 27 2018

Select[Prime[Range[500]], Mod[#, 14] == 1 &]  (* Harvey P. Dale, Mar 21 2011 *)

is(n)=isprime(n) && n%14==1 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 6n log n. - Charles R Greathouse IV, Jul 02 2016

Simpler definition from N. J. A. Sloane, Jul 11 2008

A141887 Primes congruent to 19 mod 20.

Original entry on oeis.org

19, 59, 79, 139, 179, 199, 239, 359, 379, 419, 439, 479, 499, 599, 619, 659, 719, 739, 839, 859, 919, 1019, 1039, 1259, 1279, 1319, 1399, 1439, 1459, 1499, 1559, 1579, 1619, 1699, 1759, 1879, 1979, 1999, 2039, 2099, 2179, 2239, 2339, 2399, 2459, 2539, 2579, 2659

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A105854, A141881, A141882, A141883.

[p: p in PrimesUpTo(3000) | p mod 20 eq 19 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[19,5000,20],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)

is(n)=isprime(n) && n%20==19 \\ Charles R Greathouse IV, Jul 01 2016

A141885 Primes congruent to 13 mod 20.

Original entry on oeis.org

13, 53, 73, 113, 173, 193, 233, 293, 313, 353, 373, 433, 593, 613, 653, 673, 733, 773, 853, 953, 1013, 1033, 1093, 1153, 1193, 1213, 1373, 1433, 1453, 1493, 1553, 1613, 1693, 1733, 1753, 1873, 1913, 1933, 1973, 1993, 2053, 2113, 2153, 2213, 2273, 2293, 2333, 2393

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A105854, A141881, A141882, A141883.

[p: p in PrimesUpTo(3000) | p mod 20 eq 13 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[13,5000,20],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)

is(n)=isprime(n) && n%20==13 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 8n log n. - Charles R Greathouse IV, Jul 02 2016

A102851 Primes of the form 19n + 5.

Original entry on oeis.org

5, 43, 157, 233, 271, 347, 461, 499, 613, 727, 1031, 1069, 1259, 1297, 1373, 1487, 1601, 1753, 1867, 2399, 2437, 2551, 2741, 2969, 3083, 3121, 3463, 3539, 3691, 3767, 3881, 3919, 4261, 4337, 4451, 4603, 4679, 4793, 4831, 5021, 5059, 5477, 5591, 5743

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 28 2005

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

Cf. A105854, A141881, A141882, A141883.

[ a: n in [0..400] | IsPrime(a) where a is 19*n+5 ]; // Vincenzo Librandi, Jul 19 2012

Select[Range[5,5000,19],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)
Select[Table[19*n+5,{n,0,1500}],PrimeQ] (* Vincenzo Librandi, Jul 19 2012 *)

A141869 Primes congruent to 2 mod 19.

Original entry on oeis.org

2, 59, 97, 173, 211, 401, 439, 743, 857, 971, 1009, 1123, 1237, 1427, 1579, 1693, 1997, 2111, 2339, 2377, 2719, 2833, 2909, 3023, 3061, 3137, 3251, 3517, 3593, 3631, 3821, 4049, 4201, 4391, 4657, 4733, 4999, 5113, 5189, 5227, 5303, 5417, 5531, 5569, 5683

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A105854, A141881, A141882, A141883.

[p: p in PrimesUpTo(6000) | p mod 19 eq 2]; // Vincenzo Librandi, Aug 06 2012

Select[Range[2,5000,19],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)

is(n)=isprime(n) && n%19==2 \\ Charles R Greathouse IV, Jul 02 2016

{2} UNION A142152. - R. J. Mathar, Jul 20 2008

a(n) ~ 18n log n. - Charles R Greathouse IV, Jul 02 2016

A141886 Primes congruent to 17 mod 20.

Original entry on oeis.org

17, 37, 97, 137, 157, 197, 257, 277, 317, 337, 397, 457, 557, 577, 617, 677, 757, 797, 857, 877, 937, 977, 997, 1097, 1117, 1217, 1237, 1277, 1297, 1597, 1637, 1657, 1697, 1777, 1877, 1997, 2017, 2137, 2237, 2297, 2357, 2377, 2417, 2437, 2477, 2557, 2617, 2657

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A105854, A141881, A141882, A141883.

[p: p in PrimesUpTo(3000) | p mod 20 eq 17 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[17,5000,20],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)

is(n)=isprime(n) && n%20==17 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 8n log n. - Charles R Greathouse IV, Jul 02 2016

cp's OEIS Frontend

A124826 Primes congruent to 1 mod 21.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A141882 Primes congruent to 7 mod 20.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A141883 Primes congruent to 9 mod 20.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A122072 Greatest prime less than 10n.

Views

Author

Keywords

Comments

Links

Programs

Mathematica

PARI

A140444 Primes congruent to 1 (mod 14).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Formula

Extensions

A141887 Primes congruent to 19 mod 20.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A141885 Primes congruent to 13 mod 20.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A102851 Primes of the form 19n + 5.

Views

Author

Keywords