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

%I A351140 #25 Nov 21 2023 11:51:23
%S A351140 1,5,11,17,23,31,41,53,67,79,97,113,127,149,167,191,211,233,257,281,
%T A351140 307,331,359,389,419,449,479,509,541,577,613,647,683,719,757,797,839,
%U A351140 881,929,971,1013,1061,1109,1163,1213,1277,1327,1381,1433,1487,1543,1597
%N A351140 a(1) = 1, a(n) = smallest prime > a(n-1) + n.
%C A351140 The sequence with >= in place of > is essentially the same after the first three terms: 1, 3, 7, 11, 17, 23, 31, ...
%H A351140 Robert Israel, <a href="/A351140/b351140.txt">Table of n, a(n) for n = 1..10000</a>
%e A351140 The smallest prime above 1+2 is 5, so a(2)=5.
%e A351140 The smallest prime above 5+3 is 11, so a(3)=11.
%p A351140 R:= 1: p:= 1:
%p A351140 for n from 2 to 100 do
%p A351140   p:= nextprime(p+n);
%p A351140   R:= R,p;
%p A351140 od:
%p A351140 R; # _Robert Israel_, Nov 20 2023
%t A351140 a[1] = 1; a[n_] := a[n] = NextPrime[a[n - 1] + n]; Array[a, 50] (* _Amiram Eldar_, Feb 03 2022 *)
%o A351140 (Python)
%o A351140 from sympy import nextprime
%o A351140 p = 1
%o A351140 for i in range(2,1000):
%o A351140   print(p, end=",")
%o A351140   p = nextprime(p+i)
%o A351140 (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 A351140 Cf. A000040, A055498, A093503.
%K A351140 nonn
%O A351140 1,2
%A A351140 _Alex Ratushnyak_, Feb 02 2022