A291141 - OEIS

A291141

a(1) = 3 and a(n+1) is the least prime greater than a(n) + 2n such that a(n+1) + 2n + 2 is prime.

3, 7, 13, 23, 37, 59, 83, 151, 173, 251, 331, 359, 431, 463, 541, 587, 643, 683, 773, 823, 877, 947, 1051, 1103, 1163, 1231, 1307, 1367, 1429, 1489, 1559, 1657, 1723, 1811, 1933, 2011, 2087, 2221, 2311, 2393, 2539, 2647, 2801, 2953, 3079, 3209

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OFFSET

1,1

COMMENTS

a(n) > n^2 + n, so the sum of the reciprocals of the terms of this sequence converges: 1/3 + 1/7 + 1/13 + 1/23 + 1/37 + ... = 0.720731....

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

PROG

(PARI) {

p=2;

forstep(n=2, 100, 2,

p=nextprime(p+1);

while(!isprime(p+n), p=nextprime(p+1));

print1(p", "); p=p+n;

)

}

(PARI) first(n)=my(v=vector(n)); v[1]=3; for(k=2, n, forprime(p=v[k-1]+2*k, , if(isprime(p+2*k), v[k]=p; break))); v \\ Charles R Greathouse IV, Sep 13 2017

CROSSREFS

Sequence in context: A256309 A058682 A081995 * A053599 A212146 A136851

Adjacent sequences: A291138 A291139 A291140 * A291142 A291143 A291144

KEYWORD

nonn

AUTHOR

Dimitris Valianatos, Aug 18 2017

STATUS

approved