A141883 -id:A141883 - cp's OEIS frontend

A141881 Primes congruent to 1 mod 20.

41, 61, 101, 181, 241, 281, 401, 421, 461, 521, 541, 601, 641, 661, 701, 761, 821, 881, 941, 1021, 1061, 1181, 1201, 1301, 1321, 1361, 1381, 1481, 1601, 1621, 1721, 1741, 1801, 1861, 1901, 2081, 2141, 2161, 2221, 2281, 2341, 2381, 2441, 2521, 2621, 2741, 2801

Offset: 1

N. J. A. Sloane, Jul 11 2008

Such a prime is representable by either both or neither of the quadratic forms x^2 + 20 y^2 and x^2 + 100 y^2. See the Brink link. - Robert Israel, Jun 11 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893

Cf. A000040, A105854, A141882, A141883.

[p: p in PrimesUpTo(3000) | p mod 20 eq 1 ]; // Vincenzo Librandi, Aug 15 2012

select(isprime,[seq(20*i+1,i=1..1000)]); # Robert Israel, Jun 11 2014

Select[Range[1,5000,20],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 31 2011*)
Select[Prime[Range[500]],Mod[#,20]==1&] (* Harvey P. Dale, Nov 23 2024 *)

is(n)=isprime(n) && n%20==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

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

A325073 Prime numbers congruent to 9 modulo 20 representable by x^2 + 20*y^2.

Original entry on oeis.org

29, 89, 229, 349, 509, 709, 769, 809, 1009, 1049, 1109, 1229, 1249, 1289, 1409, 1549, 1669, 1709, 1789, 2029, 2069, 2089, 2389, 2729, 3049, 3089, 3169, 3329, 3389, 3469, 3529, 3929, 3989, 4049, 4229, 4289, 4549, 4649, 4729, 4789, 5009, 5209, 5669, 5689, 5849

Offset: 1

Rémy Sigrist, Mar 27 2019

nonn

Brink showed that prime numbers congruent to 9 modulo 20 are representable by exactly one of the quadratic forms x^2 + 20*y^2 or x^2 + 100*y^2. This sequence corresponds to those representable by the first form, and A325074 corresponds to those representable by the second form.

			Regarding 1009:
- 1009 is a prime number,
- 1009 = 50*20 + 9,
- 1009 = 17^2 + 20*6^2,
- hence 1009 belongs to this sequence.

David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893.
Rémy Sigrist, PARI program for A325073
Wikipedia, Kaplansky's theorem on quadratic forms

See A325067 for similar results.

Cf. A141883, A325074.

PARI
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See Links section.
```

A325074 Prime numbers congruent to 9 modulo 20 representable by x^2 + 100*y^2.

Original entry on oeis.org

109, 149, 269, 389, 409, 449, 569, 829, 929, 1069, 1129, 1429, 1489, 1609, 1889, 1949, 2129, 2269, 2309, 2549, 2609, 2689, 2749, 2789, 2909, 2969, 3109, 3209, 3229, 3449, 3709, 3769, 3889, 4129, 4349, 4409, 4889, 4909, 4969, 5189, 5309, 5449, 5569, 5749, 6029

Offset: 1

Rémy Sigrist, Mar 27 2019

nonn

Brink showed that prime numbers congruent to 9 modulo 20 are representable by exactly one of the quadratic forms x^2 + 20*y^2 or x^2 + 100*y^2. A325073 corresponds to those representable by the first form, and this sequence corresponds to those representable by the second form.

			Regarding 4409:
- 4409 is a prime number,
- 4409 = 220*20 + 9,
- 4409 = 53^2 + 100*4^2,
- hence 4409 belongs to this sequence.

David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893.
Rémy Sigrist, PARI program for A325074
Wikipedia, Kaplansky's theorem on quadratic forms

See A325067 for similar results.

Cf. A141883, A325073.

PARI
```
See Links section.
```

A244767 Prime numbers ending in the prime number 29.

Original entry on oeis.org

29, 229, 829, 929, 1129, 1229, 1429, 2029, 2129, 2729, 3229, 3329, 3529, 3929, 4129, 4229, 4729, 6029, 6229, 6329, 6529, 6829, 7129, 7229, 7529, 7829, 8329, 8429, 8629, 8929, 9029, 9629, 9829, 9929, 10429, 10529, 10729, 11329, 12329, 12829, 13229, 13729

Offset: 1

Vincenzo Librandi, Jul 06 2014

Also primes of the form 100*n+29. Subsequence of A141883, A141930.

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

Cf. A141883, A141930.

Cf. similar sequences listed in A244763.

[n: n in PrimesUpTo(16000) | n mod 100 eq 29];

Select[Prime[Range[5, 6000]], Take[IntegerDigits[#], -2]=={2, 9} &]
Select[Prime[Range[6000]],Mod[#,100]==29&] (* Harvey P. Dale, Oct 05 2021 *)

select(x->(x % 100)==29, primes(2000)) \\ Michel Marcus, Jul 06 2014

cp's OEIS Frontend

A141881 Primes congruent to 1 mod 20.

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A141882 Primes congruent to 7 mod 20.

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A141887 Primes congruent to 19 mod 20.

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A141885 Primes congruent to 13 mod 20.

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A102851 Primes of the form 19n + 5.

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A141869 Primes congruent to 2 mod 19.

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A141886 Primes congruent to 17 mod 20.

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Magma

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A325073 Prime numbers congruent to 9 modulo 20 representable by x^2 + 20*y^2.

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