A135731 -id:A135731 - cp's OEIS frontend

A135732 Distances to next prime associated with A135731.

2, 1, 3, 1, 3, 1, 3, 5, 1, 5, 3, 1, 3, 5, 5, 1, 5, 3, 1, 5, 3, 5, 7, 3, 1, 3, 1, 3, 13, 3, 5, 1, 9, 1, 5, 5, 3, 5, 5, 1, 9, 1, 3, 1, 11, 11, 3, 1, 3, 5, 1, 9, 5, 5, 5, 1, 5, 3, 1, 9, 13, 3, 1, 3, 13, 5, 9, 1, 3, 5, 7, 5, 5, 3, 5, 7, 3, 7, 9, 1, 9, 1, 5, 3, 5, 7, 3, 1, 3, 11, 7, 3, 7, 3, 5, 11

Offset: 1

Enoch Haga, Nov 26 2007

Essentially the same as A046933. [From R. J. Mathar, Oct 28 2008]

			a(2)=3 because when n=8 (8 is next n after prime 7), next prime is 11 and distance is 3

Cf. A135731.

Beginning with prime=2, the first n after 2 is 3 and from n=3 to next prime >n is 5, with distance from 3 to 5=2. Next n after prime=5 is 6, so that distance to next prime 7 = 1.

A175216 The first nonprimes after the primes.

Original entry on oeis.org

4, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 128, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272

Offset: 1

Jaroslav Krizek, Mar 06 2010

Essentially the same as A135731, A055670, A028815 and A008864. [R. J. Mathar, Mar 13 2010]

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000040, A008864, A028815, A055670, A135731.

[n eq 1 select 4 else NthPrime(n) +1: n in [1..100]]; // G. C. Greubel, Aug 06 2024

Table[Prime[n] +1 +Boole[n==1], {n,100}] (* G. C. Greubel, Aug 06 2024 *)

def A175216(n): return nth_prime(n) +1 +int(n==1)
[A175216(n) for n in range(1,101)] # G. C. Greubel, Aug 06 2024

a(1) = 4, for n >= 2, a(n) = A008864(n) = A000040(n) + 1.

A299763 a(n) = 1 + A182986(n).

Original entry on oeis.org

1, 3, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 128, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284

Offset: 1

Omar E. Pol, Mar 14 2018

Are these the indices of the rows of A299762 where there is a record?

G. C. Greubel, Table of n, a(n) for n = 1..10000

First differences are in A054541.
Cf. A008864, A028815, A182986, A299762.
Essentially the same as A008864, A028815, A055670, A135731, A175216.

A299763:= func< n | n eq 1 select 1 else NthPrime(n-1) + 1 >;
[A299763(n): n in [1..70]]; // G. C. Greubel, Aug 05 2024

A299763[n_]:= If[n==1, 1, Prime[n-1] +1];
Table[A299763[n], {n,70}] (* G. C. Greubel, Aug 05 2024 *)

def A299763(n): return 1 if n==1 else nth_prime(n-1) + 1
[A299763(n) for n in range(1,71)] # G. C. Greubel, Aug 05 2024

a(n) = A028815(n-1) - [n=1].

a(n) = A008864(n-1) for n >= 2, with a(1) = 1.

A122825 a(n) = n + number of previous prime terms, a(1) = 1.

Original entry on oeis.org

1, 2, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94

Offset: 1

Zak Seidov, Oct 23 2006

nonn

Or, a(1)=1; a(n)=a(n-1) + d: if a(n-1) is prime then d=2 otherwise d=1.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A135731 (complement).

s={1};p=0;Do[b=n+p;AppendTo[s,b];If[PrimeQ[b],p++ ],{n,2,130}];s

lista(nn) = {print1(a=1, ", "); nbp = 0; for (n=2, nn, newn = nbp + n; print1(newn, ", "); nbp += isprime(newn););} \\ Michel Marcus, Jul 31 2017

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A135732 Distances to next prime associated with A135731.

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A175216 The first nonprimes after the primes.

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Magma

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A299763 a(n) = 1 + A182986(n).

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A122825 a(n) = n + number of previous prime terms, a(1) = 1.

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