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

2,2

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.

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A080147, A080148.

Sequence in context: A104752 A343745 A183000 * A096667 A265989 A225847

Adjacent sequences: A170818 A170819 A170820 * A170822 A170823 A170824

Keyword

nonn,look

Author

N. J. A. Sloane, Dec 24 2009

Status

approved