A142137 -id:A142137 - cp's OEIS frontend

A142138 Primes congruent to 29 mod 37.

29, 103, 251, 547, 769, 991, 1213, 1361, 1583, 1657, 1879, 2027, 2693, 2767, 3137, 3359, 3433, 3581, 3803, 3877, 4099, 4691, 4987, 5209, 5431, 5653, 5801, 6689, 6763, 6911, 7207, 7577, 7873, 8243, 8317, 8539, 8761, 9649, 9871, 10093, 10463, 11351, 12239, 12757

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A142136, A142137.

[p: p in PrimesUpTo(15000) | p mod 37 eq 29 ]; // Vincenzo Librandi, Aug 19 2012

Select[Range[29,30000,37],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 12 2011 *)
Select[Prime[Range[5000]],MemberQ[{29},Mod[#,37]]&] (* Vincenzo Librandi, Aug 19 2012 *)

is(n)=isprime(n) && n%37==29 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 36n log n. - Charles R Greathouse IV, Jul 02 2016

A142139 Primes congruent to 30 mod 37.

Original entry on oeis.org

67, 659, 733, 881, 1103, 1399, 1621, 2213, 2287, 2657, 2731, 2879, 2953, 3323, 3767, 3989, 4211, 4507, 4729, 4877, 4951, 5099, 5839, 5987, 6653, 6949, 7393, 7541, 8059, 8429, 9391, 9539, 9613, 10427, 10501, 10723, 11093, 11833, 11981, 12203, 12277, 12647

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A142137, A142138.

[p: p in PrimesUpTo(15000) | p mod 37 eq 30 ]; // Vincenzo Librandi, Aug 19 2012

Select[Range[30,30000,37],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 12 2011 *)
Select[Prime[Range[5000]],MemberQ[{30},Mod[#,37]]&] (* Vincenzo Librandi, Aug 19 2012 *)

is(n)=isprime(n) && n%37==30 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 36n log n. - Charles R Greathouse IV, Jul 03 2016

A301619 Primes congruent to 65 (mod 192).

Original entry on oeis.org

257, 449, 641, 1217, 1409, 1601, 2753, 3137, 3329, 4289, 4481, 4673, 5441, 6977, 7937, 8513, 9281, 9473, 9857, 10433, 11393, 11777, 11969, 12161, 13121, 13313, 13697, 14081, 14657, 15233, 15809, 16001, 16193, 17729, 17921, 19073, 19457, 19841, 21377, 21569

Offset: 1

Felix Fröhlich, Mar 24 2018

In other words, primes of the form 192*k+65 for k > 0.

R. Scott and R. Styer, On p^x - q^y = c and related three term exponential Diophantine equations with prime bases, Journal of Number Theory, Vol. 105, No. 2 (2004), 212-234. See p. 218.

Subsequence of A002144 (primes of form 4*k+65) and A007519 (primes of form 8*k+65).

Cf. primes congruent to 65 (mod k): A142068 (k=66), A142137 (k=74), A142221 (k=82), A142271 (k=86), A142369 (k=94), A142427 (k=98), A142485 (k=102), A142542 (k=106), A142670 (k=114), A142733 (k=118), A142802 (k=122), A142890 (k=126), A105129 (k=128).

[p: p in PrimesUpTo(25000) | p mod 192 in {65}]; // Vincenzo Librandi, Jan 04 2020

Select[Prime[Range[2500]], MemberQ[{65}, Mod[#, 192]] &] (* Vincenzo Librandi, Jan 04 2020 *)

forprime(p=1, 5e4, if(Mod(p, 192)==65, print1(p, ", ")))

cp's OEIS Frontend

A142138 Primes congruent to 29 mod 37.

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A142139 Primes congruent to 30 mod 37.

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Magma

Mathematica

PARI

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A301619 Primes congruent to 65 (mod 192).

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Magma

Mathematica

PARI