A142322 -id:A142322 - cp's OEIS frontend

A196000 Numbers k such that 90*k + 19 is prime.

0, 1, 2, 4, 8, 9, 10, 11, 14, 16, 17, 22, 23, 24, 25, 28, 30, 34, 35, 36, 39, 41, 43, 46, 48, 50, 53, 55, 56, 60, 63, 64, 65, 69, 74, 77, 78, 79, 80, 81, 83, 85, 86, 91, 93, 98, 99, 101, 102, 107, 108, 109, 111, 112, 115, 116

Offset: 1

J. W. Helkenberg, Oct 27 2011

A142322 is a digital root 1 and last digit 9 preserving sequence.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A195953, A181732, A198382.

A142322 := proc(n)
        option remember;
        if n = 1 then
                19 ;
        else
                a := nextprime(procname(n-1)) ;
                while (a mod 45) <> 19 do
                        a := nextprime(a) ;
                end do;
                return a;
        end if;
end proc:
A196000 := proc(n)
        (A142322(n)-19)/90 ;
end proc:
seq(A196000(n),n=1..80) ; # R. J. Mathar, Oct 31 2011

Select[Range[0, 120], PrimeQ[90 # + 19] &] (* Ivan Neretin, Apr 27 2017 *)

is(n)=isprime(90*n+19) \\ Charles R Greathouse IV, Apr 25 2016

a(n) = (A142322(n) - 19)/90.

A141855 Primes congruent to 8 mod 11.

Original entry on oeis.org

19, 41, 107, 151, 173, 239, 283, 349, 503, 547, 569, 613, 701, 811, 877, 1009, 1031, 1097, 1163, 1229, 1361, 1427, 1471, 1493, 1559, 1669, 1801, 1823, 1867, 1889, 1933, 1999, 2087, 2131, 2153, 2351, 2417, 2549, 2593, 2659, 2791, 2857, 2879, 3011, 3121, 3187

Offset: 1

N. J. A. Sloane, Jul 11 2008

Primes congruent to 19 mod 22. - Chai Wah Wu, Apr 29 2025

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

Cf. A142322.

[ p: p in PrimesUpTo(5000) | p mod 11 eq 8 ]; // Vincenzo Librandi, Apr 19 2011

Select[Range[19, 50000, 22], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2011 *)

is(n)=isprime(n) && n%11==8 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 10n log n. - Charles R Greathouse IV, Jul 02 2016

A142324 Primes congruent to 23 mod 45.

Original entry on oeis.org

23, 113, 293, 383, 563, 653, 743, 1013, 1103, 1193, 1283, 1373, 1553, 1733, 1823, 1913, 2003, 2273, 2543, 2633, 2903, 3083, 3533, 3623, 3803, 4073, 4253, 4523, 4703, 4793, 4973, 5153, 5333, 5693, 5783, 6053, 6143, 6323, 6863, 7043, 7583, 7673, 7853, 8123

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A142322.

[p: p in PrimesUpTo(10000) | p mod 45 eq 23]; // Vincenzo Librandi, Aug 26 2012

Select[Range[23, 30000, 90], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jul 14 2011 *)
Select[Prime[Range[1200]], MemberQ[{23}, Mod[#, 45]] &] (* Vincenzo Librandi, Aug 26 2012 *)

is(n)=isprime(n) && n%45==23 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 24n log n. - Charles R Greathouse IV, Jul 02 2016

A142730 Primes congruent to 3 mod 59.

Original entry on oeis.org

3, 239, 593, 829, 947, 1301, 2953, 3307, 3779, 4133, 4723, 5077, 5431, 5903, 6257, 7673, 8263, 8971, 9679, 10151, 10859, 11213, 12157, 12511, 12983, 13219, 13337, 13691, 14281, 14753, 15107, 15461, 16759, 17231, 17467, 17939, 19001, 19237, 19709, 20063, 20771

Offset: 1

N. J. A. Sloane, Jul 11 2008

Primes congruent to 3 mod 118. - Vladimir Joseph Stephan Orlovsky, Jul 14 2011.

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

Cf. A000040, A142322.

[p: p in PrimesUpTo(21000) | p mod 59 eq 3 ]; // Vincenzo Librandi, Sep 02 2012

Select[Range[3, 30000, 118], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jul 14 2011 *)
Select[Prime[Range[2600]], MemberQ[{3}, Mod[#, 59]] &] (* Vincenzo Librandi, Sep 02 2012 *)

is(n)=isprime(n) && n%59==3 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 58n log n. - Charles R Greathouse IV, Jul 02 2016

A142732 Primes congruent to 5 mod 59.

Original entry on oeis.org

5, 241, 359, 1303, 1657, 2011, 2129, 2719, 2837, 3191, 4253, 5197, 5669, 6967, 7321, 7793, 8147, 8501, 8737, 9091, 9209, 10271, 10861, 10979, 11923, 12041, 12277, 13103, 13339, 13457, 13693, 14401, 14519, 15227, 15581, 15817, 16879, 17351, 18059, 18413

Offset: 1

N. J. A. Sloane, Jul 11 2008

Primes congruent to 5 mod 118. - Vladimir Joseph Stephan Orlovsky, Jul 14 2011.

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

Cf. A000040, A142322.

[p: p in PrimesUpTo(19000) | p mod 59 eq 5 ]; // Vincenzo Librandi, Sep 02 2012

Select[Range[5, 30000, 118], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jul 14 2011 *)
Select[Prime[Range[2600]], MemberQ[{5}, Mod[#, 59]] &] (* Vincenzo Librandi, Sep 02 2012 *)

is(n)=isprime(n) && n%59==5 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 58n log n. - Charles R Greathouse IV, Jul 02 2016

A142327 Primes congruent to 29 mod 45.

Original entry on oeis.org

29, 389, 479, 569, 659, 839, 929, 1019, 1109, 1289, 1559, 2099, 2459, 2549, 2729, 2819, 2909, 2999, 3089, 3359, 3449, 3539, 3719, 3989, 4079, 4259, 4349, 4799, 4889, 5519, 5879, 6329, 6599, 6689, 6779, 6869, 6959, 7229, 7499, 7589, 7949, 8039, 8219, 8669

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A142322.

[p: p in PrimesUpTo(10000) | p mod 45 eq 29]; // Vincenzo Librandi, Aug 26 2012

Select[Range[29, 30000, 90], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jul 14 2011 *)
Select[Prime[Range[1200]],MemberQ[{29},Mod[#,45]]&] (* Vincenzo Librandi, Aug 26 2012 *)

is(n)=isprime(n) && n%45==29 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 24n log n. - Charles R Greathouse IV, Jul 02 2016

A142858 Primes congruent to 60 mod 61.

Original entry on oeis.org

487, 853, 1097, 1951, 2683, 2927, 3049, 3659, 4391, 4513, 6221, 6343, 6709, 8539, 8783, 10247, 10369, 10613, 10979, 11467, 11833, 12809, 13297, 13907, 14029, 14639, 15493, 15737, 15859, 16103, 18787, 19031, 19763, 20129, 20983, 21227, 22447, 22691, 23057

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A142322.

[p: p in PrimesUpTo(24000) | p mod 61 eq 60 ] ; // Vincenzo Librandi, Sep 06 2012

Select[Range[60, 30000, 61], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jul 14 2011 *)
Select[Prime[Range[2800]], MemberQ[{60}, Mod[#, 61]] &] (* Vincenzo Librandi, Sep 06 2012 *)

is(n)=isprime(n) && n%61==60 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 60n log n. - Charles R Greathouse IV, Jul 03 2016

A142786 Primes congruent to 7 mod 60.

Original entry on oeis.org

7, 67, 127, 307, 367, 487, 547, 607, 727, 787, 907, 967, 1087, 1327, 1447, 1567, 1627, 1747, 1867, 1987, 2287, 2347, 2467, 2647, 2707, 2767, 2887, 3067, 3187, 3307, 3547, 3607, 3727, 3847, 3907, 3967, 4027, 4327, 4447, 4507, 4567, 4987, 5107, 5167, 5227

Offset: 1

N. J. A. Sloane, Jul 11 2008

Comment from Joshua S.M. Weiner, Oct 12 2012 (Start)
Intersection of A068229 and A141882. Subsequence of A132231.
Congruence classes of primes mod 60: A088955 (1), (this sequence 7),  A117047 (11), A142787 (13), A142788 (17), A142789 (19), A142790 (23), A142791 (29), A142792 (31), A142793 (37), A142794 (41), A142795 (43), A142796 (47), A142797 (49), A142798 (53), A142799 (59). (End)

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

Cf. A000040, A142322.

[p: p in PrimesUpTo(6000) | p mod 60 eq 7 ]; // Vincenzo Librandi, Sep 04 2012

Select[Prime[Range[1000]], Mod[#, 60] == 7 &] (* T. D. Noe, Oct 12 2012 *)
Select[Range[7,5300,60],PrimeQ] (* Harvey P. Dale, Nov 21 2018 *)

cp's OEIS Frontend

A196000 Numbers k such that 90*k + 19 is prime.

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A141855 Primes congruent to 8 mod 11.

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Magma

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A142324 Primes congruent to 23 mod 45.

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Magma

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A142730 Primes congruent to 3 mod 59.

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Magma

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A142732 Primes congruent to 5 mod 59.

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Magma

Mathematica

PARI

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A142327 Primes congruent to 29 mod 45.

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Magma

Mathematica

PARI

Formula

A142858 Primes congruent to 60 mod 61.

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Programs

Magma

Mathematica