A087274 -id:A087274 - cp's OEIS frontend

A087963 Exponent of highest power of 2 dividing 3*prime(n)+1.

0, 1, 4, 1, 1, 3, 2, 1, 1, 3, 1, 4, 2, 1, 1, 5, 1, 3, 1, 1, 2, 1, 1, 2, 2, 4, 1, 1, 3, 2, 1, 1, 2, 1, 6, 1, 3, 1, 1, 3, 1, 5, 1, 2, 4, 1, 1, 1, 1, 4, 2, 1, 2, 1, 2, 1, 3, 1, 6, 2, 1, 4, 1, 1, 2, 3, 1, 2, 1, 3, 2, 1, 1, 5, 1, 1, 4, 3, 2, 2, 1, 4, 1, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 3, 1, 3, 1, 2, 1

Offset: 1

Labos Elemer, Sep 18 2003

nonn

			For n = 10: p = prime(10) = 29, 3*p + 1 = 88 = 2^3 * 11, a(10) = 3.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A087272, A087273, A087274, A007814, A087230.

[Valuation(3*NthPrime(n)+1, 2): n in [1..80]]; // Vincenzo Librandi, Sep 01 2016

ffi[x_] := Flatten[FactorInteger[x]]; e2[x_] := Part[[ffi[x]], 2]; Table[e2[3*Prime[w]+1], {w, 1, 100}]
IntegerExponent[3 * Prime[Range[100]] + 1, 2] (* Amiram Eldar, Jul 12 2024 *)

a(n) = valuation(3*prime(n)+1, 2); \\ Michel Marcus, Sep 01 2016

from sympy import prime
def A087963(n): return (~(m:=prime(n)*3+1)&m-1).bit_length() # Chai Wah Wu, Jul 10 2022

a(n) = A007814(3*prime(n)+1).

a(1)=0 corrected by Michel Marcus, Sep 01 2016

A087964 a(n) is the least prime p such that exponent of highest power of 2 dividing 3p+1 equals n.

Original entry on oeis.org

3, 17, 13, 5, 53, 149, 1237, 1109, 853, 2389, 3413, 17749, 128341, 70997, 251221, 415061, 218453, 2708821, 27088213, 29709653, 3495253, 85284181, 13981013, 39146837, 794121557, 1498764629, 492131669, 626349397, 13779686741

Offset: 1

Labos Elemer, Sep 18 2003

nonn

			p = 218453 is the first prime so that 3*p+1 = 655360 = (2^18)*5 has 18 as exponent of 2 in 3p+1, thus a(18) = 218453.

Giovanni Resta, Table of n, a(n) for n = 1..1000

Cf. A087272, A087273, A087274, A007814, A087230, A087963.

f:= proc(n)
   local m,t,p;
   t:= 2^n;
   for m from 1 + 4*(n mod 2) by 6 do
     p:= (t*m-1)/3;
     if isprime(p) then return p fi
   od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 18 2017

a[n_] := Module[{m, t = 2^n, p}, For[m = 1 + 4 Mod[n, 2], True, m += 6, p = (t m - 1)/3; If[PrimeQ[p], Return[p]]]];
Array[a, 100] (* Jean-François Alcover, Aug 28 2020, after Robert Israel *)

a(n) = A000040(Min{x; A007814(1 + 3*A000040(x)) = n}).

More terms from Ray Chandler, Sep 21 2003

cp's OEIS Frontend

A087963 Exponent of highest power of 2 dividing 3*prime(n)+1.

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