A074973 - OEIS

A074973

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

1, 4, 11, 20, 17, 67, 104, 56, 125, 165, 182, 316, 236, 359, 407, 1254, 667, 836, 1521, 1210, 1966, 3197, 1520, 2294, 2279, 2046, 5410, 5472, 1965, 6702, 13947, 10138, 12122, 16760, 7659, 22325, 16784, 13072, 36169, 17852, 15414, 69872, 23814, 16370, 46752

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OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

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

PROG

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

(Magma)

S:=[];

i:=1;

for n in [1..45] do

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

i:=i+1;

end while;

Append(~S, i);

i:=1;

end for;

S; // Bruno Berselli, Oct 03 2013

CROSSREFS

Cf. A059787.

Sequence in context: A009908 A321643 A049935 * A327457 A025526 A301093

Adjacent sequences: A074970 A074971 A074972 * A074974 A074975 A074976

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 06 2002

EXTENSIONS

a(44)-a(45) from Bruno Berselli, Oct 03 2013

STATUS

approved