A170821 Let p = n-th prime; a(n) = smallest k >= 0 such that 4k == 3 mod p.

0, 2, 6, 9, 4, 5, 15, 18, 8, 24, 10, 11, 33, 36, 14, 45, 16, 51, 54, 19, 60, 63, 23, 25, 26, 78, 81, 28, 29, 96, 99, 35, 105, 38, 114, 40, 123, 126, 44, 135, 46, 144, 49, 50, 150, 159, 168, 171, 58, 59, 180, 61, 189, 65, 198, 68, 204, 70, 71, 213, 74, 231, 234, 79, 80, 249, 85, 261

Offset: 2

Author

N. J. A. Sloane, Dec 24 2009

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 2..10000
• I. Anderson and D. A. Preece, Combinatorially fruitful properties of 3*2^(-1) and 3*2^(-2) modulo p, Discr. Math., 310 (2010), 312-324.

Crossrefs

Cf. A000040, A080147, A080148.

Programs

Maple

f:=proc(n) local b; for b from 0 to n-1 do if 4*b mod n = 3 then RETURN(b); fi; od: -1; end; [seq(f(ithprime(n)),n=2..100)]; # Gives wrong answer for n=2.
# Alternative:
f:= n -> 3/4 mod ithprime(n):
map(f, [$2..100]); # Robert Israel, Dec 03 2018

Mathematica

a[n_] := If[n<3, 0, Module[{p=Prime[n], k=0}, While[Mod[4k, p] != 3, k++]; k]]; Array[a, 100,2] (* Amiram Eldar, Dec 03 2018 *)

PARI

a(n) = my(p=prime(n), k=0); while(Mod(4*k, p) != 3, k++); k; \\ Michel Marcus, Dec 03 2018

Formula

a(n) = (prime(n)+3)/4 if n is in A080147, (3*prime(n)+3)/4 if n is in A080148 (except for n=2). - Robert Israel, Dec 03 2018