A267101 2 followed by permutation of odd primes, where each n-th prime of the form 4k+1 (A002144) has been replaced with the n-th prime of the form 4k+3 (A002145) and vice versa.

2, 5, 3, 13, 17, 7, 11, 29, 37, 19, 41, 23, 31, 53, 61, 43, 73, 47, 89, 97, 59, 101, 109, 67, 71, 79, 113, 137, 83, 103, 149, 157, 107, 173, 127, 181, 131, 193, 197, 139, 229, 151, 233, 163, 167, 241, 257, 269, 277, 179, 191, 281, 199, 293, 211, 313, 223, 317, 227, 239, 337, 251, 349, 353, 263, 271, 373, 283, 389

Offset: 1

Author

Antti Karttunen, Feb 01 2016

Keywords

• nonn

Comments

After 2, for each n >= 1, swap the places of primes A002144(n) and A002145(n) in A000040.

Examples

			For n=2, for which A000040(2) = 3, the first prime of the form 4k+3, we select the first prime of the form 4k+1, which is 5, thus a(2) = 5.
For n=3, for which A000040(3) = 5, the first prime of the form 4k+1, we select the first prime of the form 4k+3, which is 3, thus a(3) = 3.
For n=4, for which A000040(4) = 7, the second prime of the form 4k+3, we select the second prime of the form 4k+1, which is 13, thus a(4) = 13.
For n=5, for which A000040(5) = 11, the third prime of the form 4k+3, we select the third prime of the form 4k+1, which is 17, thus a(5) = 17.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A000040, A002144, A002145, A267097, A267098, A267099, A267100.

Cf. also A108546.

Programs

Scheme

(define (A267101 n) (cond ((= 1 n) 2) ((= 1 (modulo (A000040 n) 4)) (A002145 (A267097 n))) (else (A002144 (A267098 n)))))

Formula

a(1) = 2; after which, if prime(n) modulo 4 = 1, a(n) = A002145(A267097(n)), otherwise a(n) = A002144(A267098(n)).

a(n) = A000040(A267100(n)).

a(n) = A267099(A000040(n)).