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A362222 Slowest increasing sequence where a(n) + n^2 is a prime.

%I A362222 #17 Apr 16 2023 20:27:20
%S A362222 1,3,4,7,12,17,18,19,20,27,28,29,30,31,32,37,42,43,48,49,50,57,58,65,
%T A362222 66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,93,96,97,100,103,104,
%U A362222 105,124,133,138,147,148,153,154,163,166,171,184,193,196,197,198,205
%N A362222 Slowest increasing sequence where a(n) + n^2 is a prime.
%H A362222 Michael S. Branicky, <a href="/A362222/b362222.txt">Table of n, a(n) for n = 1..10000</a>
%e A362222 a(2) = 3, since the smallest number greater than all the previous terms which gives a prime when added to 2^2 is 3.
%p A362222 R:= 1: t:= 1:
%p A362222 for n from 2 to 100 do
%p A362222   t:= nextprime(t+n^2)-n^2;
%p A362222   R:= R,t
%p A362222 od:
%p A362222 R; # _Robert Israel_, Apr 11 2023
%t A362222 a[n_] := a[n] = Module[{k = a[n - 1] + 1}, While[! PrimeQ[n^2 + k], k++]; k]; a[0] = 0; Array[a, 100] (* _Amiram Eldar_, Apr 12 2023 *)
%o A362222 (PARI) seq(n)={my(a=vector(n), p=0); for(n=1, #a, p++; while(!isprime(p+n^2), p++); a[n]=p); a} \\ _Andrew Howroyd_, Apr 11 2023
%o A362222 (Python)
%o A362222 from sympy import nextprime
%o A362222 from itertools import count, islice
%o A362222 def agen(): # generator of terms
%o A362222     an = 1
%o A362222     for n in count(2):
%o A362222         yield an
%o A362222         an = nextprime(an + n**2) - n**2
%o A362222 print(list(islice(agen(), 62))) # _Michael S. Branicky_, Apr 16 2023
%Y A362222 Cf. A053000, A107819.
%K A362222 nonn
%O A362222 1,2
%A A362222 _Angad Singh_, Apr 11 2023