A084308 Duplicate of A067605.
2, 6, 11, 24, 42, 121, 30, 319, 99, 1592, 344, 574, 3786, 4196, 650, 4619, 217, 1532
Offset: 1
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a(4) = 89 because gcd(89-1, 97-1) = gcd(8*11, 8*16) = 8 = 2*4 and these primes are the smallest with this property. a(49) = 604073 because gcd(604073-1, 604171-1) = gcd(6164*98, 6165*98) = 98 = 2*49.
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
With[{tsp={#[[1]],#[[2]],GCD[#[[1]]-1,#[[2]]-1]}&/@Partition[Prime[ Range[ 300000]],2,1]}, Transpose[Flatten[Table[Select[tsp, Last[#]==2n&,1],{n,40}],1]][[1]]] (* Harvey P. Dale, Jul 07 2013 *)
list(len) = {my(v = vector(len), c = 0, p = 3, i); forprime(q = 5, , i = gcd(p-1, q-1)/2; if(i <= len && v[i] == 0, v[i] = p; c++; if(c == len, break)); p = q); v;} \\ Amiram Eldar, Mar 05 2025
For n = 2: a(2) = 6 = A067605(2). For n = 3: a(3) = 24 means: firstly occurs that for three consecutive p-1 terms GCD[prime(24)-1, prime(25)-1, prime(26)-1] = GCD[88, 96, 100] = 4 > 2;
a(n) = {my(k = 0, v = vector(n, i, prime(i)-1)); if(gcd(v) > 2, return(0)); forprime(p = v[n]+1, , k++; v = concat(vecextract(v, "^1"), p-1); if(gcd(v) > 2, return(k)));} \\ Amiram Eldar, Jun 22 2024
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