A105129 -id:A105129 - cp's OEIS frontend

A301619 Primes congruent to 65 (mod 192).

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, ", ")))

A339900 Lexicographically earliest permutation of odd primes such that A007814(a(n)-1) = 1+A007814(n), where A007814 gives the 2-adic valuation of n.

Original entry on oeis.org

3, 5, 7, 41, 11, 13, 19, 17, 23, 29, 31, 73, 43, 37, 47, 97, 59, 53, 67, 89, 71, 61, 79, 113, 83, 101, 103, 137, 107, 109, 127, 193, 131, 149, 139, 233, 151, 157, 163, 241, 167, 173, 179, 281, 191, 181, 199, 353, 211, 197, 223, 313, 227, 229, 239, 337, 251, 269, 263, 409, 271, 277, 283, 641, 307, 293, 311, 457, 331

Offset: 1

Antti Karttunen, Dec 25 2020

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A001511, A007814, A065091.
Cf. A002145 (odd bisection), A007521 (quadrisection starting from 5), A105126, A105127, A105128, A105129, A105130, A105131, A105132.
Cf. also A108546, A111745.

A339900(n) = { my(lev=1+valuation(n,2), k=(1+(n>>(lev-1)))/2); forprime(p=3,,if(valuation(p-1,2)==lev, k--; if(!k, return(p)))); };

cp's OEIS Frontend

A301619 Primes congruent to 65 (mod 192).

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