A144309 -id:A144309 - cp's OEIS frontend

A100964 Smallest prime number that begins a prime gap of at least 2n.

3, 7, 23, 89, 113, 113, 113, 523, 523, 887, 1129, 1327, 1327, 1327, 1327, 1327, 1327, 9551, 15683, 15683, 15683, 15683, 19609, 19609, 19609, 19609, 31397, 31397, 31397, 31397, 31397, 31397, 31397, 31397, 31397, 31397, 155921, 155921, 155921, 155921

Offset: 1

T. D. Noe, Nov 23 2004

nonn

			a(5) = a(6) = a(7) = 113 because there is a gap of 14 between 113 and 127.

Amiram Eldar, Table of n, a(n) for n = 1..775

Cf. A000230, A002386, A005250, A144309.

k=1; Table[While[Prime[k+1]-Prime[k] < 2n, k++ ]; Prime[k], {n, 48}]

lista(pmax) = {my(k = 1, prv = 2, m = 2, kprv = 2); forprime(p = 3, pmax, k++; if(p - prv >= m, for(i = 1, (p - prv - m)/2 + 1, print1(prv, ", ")); m = p - prv + 2; kprv = k); prv = p);} \\ Amiram Eldar, Sep 06 2024

a(n) = prime(A144309(n)). - Michel Marcus, Nov 02 2013

A307325 a(n) is the smallest number k for which prime(k+1) - prime(k) is greater than n.

Original entry on oeis.org

2, 4, 4, 9, 9, 24, 24, 30, 30, 30, 30, 30, 30, 99, 99, 99, 99, 154, 154, 189, 189, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 217, 1183, 1183, 1831, 1831, 1831, 1831, 1831, 1831, 1831, 1831, 2225, 2225, 2225, 2225, 2225, 2225, 2225, 2225, 3385, 3385, 3385, 3385

Offset: 1

Marius A. Burtea, Apr 02 2019

nonn

For any n there is an infinity of numbers m for which prime(m+1) - prime(m) is greater than n.

It appears that the sequence of lengths of successive runs is equal to A053695. - Marc Bofill Janer, May 21 2019

			For n = 2, prime(2) - prime(1) = 3 - 2 = 1, prime(3) - prime(2) = 5 - 3 = 2, prime(5) - prime(4) = 11 - 7 = 4, so a(2) = 4.

Laurențiu Panaitopol, Dinu Șerbănescu, Number theory and combinatorial problems for juniors, Ed.Gil, Zalău, (2003), ch. 1, p.7, pr. 25. (in Romanian).

Cf. A000040, A001223, A005250, A005669.

Cf. A053695, A144309.

v=primes(1000000);
for u=1:100; ss=1;
    while and(v(ss+1)-v(ss)<=u,ss

v:=PrimesUpTo(10000000);
sol:=[];
for u in [1..60] do
   for ss in [1..#v-1] do
    if v[ss+1]-v[ss] gt u then
         sol[u]:=ss;
         break;
     end if;
   end for;
end for;
   sol;

a(n) = my(k=1); while(prime(k+1) - prime(k) <= n, k++); k; \\ Michel Marcus, Apr 03 2019

a(2*n) = a(2*n+1) = A144309(n+1) for n>=1. - Georg Fischer, Dec 05 2022

cp's OEIS Frontend

A100964 Smallest prime number that begins a prime gap of at least 2n.

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A307325 a(n) is the smallest number k for which prime(k+1) - prime(k) is greater than n.

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