A141882 -id:A141882 - 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

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

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

A244773 Prime numbers ending in the prime number 67.

Original entry on oeis.org

67, 167, 367, 467, 967, 1367, 1567, 1667, 1867, 2267, 2467, 2767, 3067, 3167, 3467, 3767, 3967, 4567, 4967, 5167, 5867, 6067, 6367, 6967, 7867, 8167, 8467, 8867, 9067, 9467, 9767, 9967, 10067, 10267, 10567, 10667, 10867, 11467, 11867, 12967, 13267

Offset: 1

Vincenzo Librandi, Jul 07 2014

Also primes of the form 100*n+67. Subsequence of A141882, A141940.

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

Cf. similar sequences listed in A244763.

Cf. A141882, A141940.

[n: n in PrimesUpTo(14000) | n mod 100 eq 67];

Select[Prime[Range[5, 6000]], Take[IntegerDigits[#], -2]=={6, 7} &]

select(x->(x % 100)==67, primes(2000)) \\ Michel Marcus, Jul 07 2014

A244770 Prime numbers ending in the prime number 47.

Original entry on oeis.org

47, 347, 547, 647, 947, 1447, 1747, 1847, 2347, 2447, 2647, 3347, 3547, 3847, 3947, 4447, 4547, 5147, 5347, 5647, 6047, 6247, 6547, 6947, 7247, 7547, 8147, 8447, 8647, 8747, 9547, 10247, 10847, 11047, 11447, 12347, 12547, 12647, 13147, 14347, 14447, 14747

Offset: 1

Vincenzo Librandi, Jul 06 2014

Also primes of the form 100*n+47. Subsequence A141882, A141944.

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

Cf. A141882, A141944.

Cf. similar sequences listed in A244763.

[n: n in PrimesUpTo(16000) | n mod 100 eq 47];

Select[Prime[Range[5, 6000]], Take[IntegerDigits[#], -2]=={4, 7} &]

select(x->(x % 100)==47, primes(2000)) \\ Michel Marcus, Jul 06 2014

A332078 Primes p = k*2^m + 1 such that k + 2^m is not prime, where k and m are the odd part and 2-valuation, respectively, of p-1.

Original entry on oeis.org

47, 67, 97, 107, 127, 137, 151, 167, 179, 181, 227, 239, 263, 283, 293, 307, 347, 349, 367, 431, 439, 457, 461, 467, 487, 491, 503, 547, 557, 571, 587, 599, 607, 617, 641, 643, 647, 661, 683, 719, 727, 733, 739, 751, 769, 787, 797, 811, 821, 823, 827, 853, 857, 887, 907

Offset: 1

M. F. Hasler, Aug 13 2020

nonn

It appears that the sequence of odd numbers k*2^m+1 such that k + 2^m is prime (A332075) mainly consists of the primes. This sequence lists the "exceptions": the complement of A332075 within the primes. (The exceptions become more frequent as the numbers grow, the asymptotic density of this subset within the primes might well approach one. See also A332079.)

These are primes of the form p = (w-2^m)*2^m + 1, where w is an odd composite number and 1 < 2^m < w. There are infinitely many primes of this form, because all primes p > 7 such that p == 7 (mod 20) are in this sequence. - Thomas Ordowski, Aug 13 2020

Robert Israel, Table of n, a(n) for n = 1..10000
Thomas Ordowski, Problem, post to the SeqFan list, August 2020.

Cf. A000040 (primes), A000265 (odd part), A007814 (2-valuation), A332075.

The terms A141882 > 7 are an infinite subsequence. - Thomas Ordowski, Aug 13 2020

filter:= proc(p) local k,m;
   if not isprime(p) then return false fi;
   m:= padic:-ordp(p-1,2);
   k:= (p-1)/2^m;
   not isprime(k+2^m);
end proc:
select(filter, [seq(i,i=3..1000,2)]); # Robert Israel, Sep 14 2020

Select[Range[1000], PrimeQ[#] && !PrimeQ[(m = 2^IntegerExponent[# - 1, 2]) + (# - 1)/m] &] (* Amiram Eldar, Aug 14 2020 *)

(A332078_upto(N)=[p|p<-primes([1,N]),!is_A332075(p)])(1000)

cp's OEIS Frontend

A141881 Primes congruent to 1 mod 20.

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A141883 Primes congruent to 9 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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Magma

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A141869 Primes congruent to 2 mod 19.

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Magma

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A141886 Primes congruent to 17 mod 20.

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Magma

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A244773 Prime numbers ending in the prime number 67.

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