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A074973 Smallest index i such that next_prime( 2*prime(i) ) - 2*prime(i) = 2n - 1. 0

%I #13 Sep 08 2022 08:45:07

%S 1,4,11,20,17,67,104,56,125,165,182,316,236,359,407,1254,667,836,1521,

%T 1210,1966,3197,1520,2294,2279,2046,5410,5472,1965,6702,13947,10138,

%U 12122,16760,7659,22325,16784,13072,36169,17852,15414,69872,23814,16370,46752

%N Smallest index i such that next_prime( 2*prime(i) ) - 2*prime(i) = 2n - 1.

%C First index i such that NextPrime[p2=2*Prime[i]]-p2 is 2n-1; case n=1 corresponds to Sophie Germain (SG) primes, others may be called SG n-primes. Distance between 2*(n-th prime) and next prime in A059787.

%e a(54) = 342337 because difference between 2*p(342337) and next prime is 2*54 -1 = 107 and 342337 is the smallest such index.

%o (PARI) a(n) = {i = 1; while (nextprime(p2=2*prime(i)) - p2 != 2*n-1, i++); i;} \\ _Michel Marcus_, Oct 03 2013

%o (Magma)

%o S:=[];

%o i:=1;

%o for n in [1..45] do

%o while not NextPrime(2*NthPrime(i))-2*NthPrime(i) eq 2*n-1 do

%o i:=i+1;

%o end while;

%o Append(~S, i);

%o i:=1;

%o end for;

%o S; // _Bruno Berselli_, Oct 03 2013

%Y Cf. A059787.

%K nonn

%O 1,2

%A _Zak Seidov_, Oct 06 2002

%E a(44)-a(45) from _Bruno Berselli_, Oct 03 2013

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)