A067605 Least k such that gcd(prime(k+1)-1, prime(k)-1) = 2n.
2, 6, 11, 24, 42, 121, 30, 319, 99, 1592, 344, 574, 3786, 4196, 650, 4619, 217, 1532, 11244, 5349, 8081, 3861, 12751, 18281, 9221, 5995, 22467, 16222, 43969, 35975, 192603, 108146, 52313, 218234, 15927, 132997, 42673, 78858, 103865, 84483, 111172, 175288, 110734
Offset: 1
Keywords
Examples
For n = 4: a(4) = 24 = gcd(89-1, 97-1) = gcd(p(24)-1, p(25)-1) = 8 = 2*4.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..183
Programs
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Maple
N:= 50: # for a(1)..a(N) V:= Vector(N): count:= 0: p:= 3: for k from 2 while count < N do q:= p; p:= nextprime(p); v:= igcd(p-1,q-1)/2; if v <= N and V[v] = 0 then count:= count+1; V[v]:= k; fi od: convert(V,list); # Robert Israel, Mar 05 2025 -
Mathematica
a = Table[0, {100}]; p = 3; q = 5; Do[q = Prime[n + 1]; d = GCD[p - 1, q - 1]/2; If[d < 101 && a[[d]] == 0, a[[d]] = n]; b = c, {n, 2, 10^7}]; a -
PARI
list(len) = {my(v = vector(len), c = 0, p = 3, k = 2, i); forprime(q = 5, , i = gcd(p-1, q-1)/2; if(i <= len && v[i] == 0, v[i] = k; c++; if(c == len, break)); p = q; k++); v;} \\ Amiram Eldar, Mar 05 2025
Formula
a(n) = PrimePi(A058264(n)).
Comments