A351140 a(1) = 1, a(n) = smallest prime > a(n-1) + n.

1, 5, 11, 17, 23, 31, 41, 53, 67, 79, 97, 113, 127, 149, 167, 191, 211, 233, 257, 281, 307, 331, 359, 389, 419, 449, 479, 509, 541, 577, 613, 647, 683, 719, 757, 797, 839, 881, 929, 971, 1013, 1061, 1109, 1163, 1213, 1277, 1327, 1381, 1433, 1487, 1543, 1597

Offset: 1

Author

Alex Ratushnyak, Feb 02 2022

Keywords

• nonn

Comments

The sequence with >= in place of > is essentially the same after the first three terms: 1, 3, 7, 11, 17, 23, 31, ...

Examples

			The smallest prime above 1+2 is 5, so a(2)=5.
The smallest prime above 5+3 is 11, so a(3)=11.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A055498, A093503.

Programs

Maple

R:= 1: p:= 1:
for n from 2 to 100 do
  p:= nextprime(p+n);
  R:= R,p;
od:
R; # Robert Israel, Nov 20 2023

Mathematica

a[1] = 1; a[n_] := a[n] = NextPrime[a[n - 1] + n]; Array[a, 50] (* Amiram Eldar, Feb 03 2022 *)

PARI

lista(nn) = my(list = List(), last = 1); listput(list, last); for (n=2, nn, last = nextprime(last + n +1); listput(list, last);); Vec(list); \\ Michel Marcus, Feb 03 2022

Python

from sympy import nextprime
p = 1
for i in range(2,1000):
  print(p, end=",")
  p = nextprime(p+i)