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a(1) = 1, a(n) = smallest prime > a(n-1) + n.
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%I #25 Nov 21 2023 11:51:23

%S 1,5,11,17,23,31,41,53,67,79,97,113,127,149,167,191,211,233,257,281,

%T 307,331,359,389,419,449,479,509,541,577,613,647,683,719,757,797,839,

%U 881,929,971,1013,1061,1109,1163,1213,1277,1327,1381,1433,1487,1543,1597

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

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

%H Robert Israel, <a href="/A351140/b351140.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p R:= 1: p:= 1:

%p for n from 2 to 100 do

%p p:= nextprime(p+n);

%p R:= R,p;

%p od:

%p R; # _Robert Israel_, Nov 20 2023

%t a[1] = 1; a[n_] := a[n] = NextPrime[a[n - 1] + n]; Array[a, 50] (* _Amiram Eldar_, Feb 03 2022 *)

%o (Python)

%o from sympy import nextprime

%o p = 1

%o for i in range(2,1000):

%o print(p, end=",")

%o p = nextprime(p+i)

%o (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

%Y Cf. A000040, A055498, A093503.

%K nonn

%O 1,2

%A _Alex Ratushnyak_, Feb 02 2022