%I #17 Apr 16 2023 20:27:20
%S 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 66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,93,96,97,100,103,104,
%U 105,124,133,138,147,148,153,154,163,166,171,184,193,196,197,198,205
%N Slowest increasing sequence where a(n) + n^2 is a prime.
%H Michael S. Branicky, <a href="/A362222/b362222.txt">Table of n, a(n) for n = 1..10000</a>
%e 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 R:= 1: t:= 1:
%p for n from 2 to 100 do
%p t:= nextprime(t+n^2)-n^2;
%p R:= R,t
%p od:
%p R; # _Robert Israel_, Apr 11 2023
%t 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 (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 (Python)
%o from sympy import nextprime
%o from itertools import count, islice
%o def agen(): # generator of terms
%o an = 1
%o for n in count(2):
%o yield an
%o an = nextprime(an + n**2) - n**2
%o print(list(islice(agen(), 62))) # _Michael S. Branicky_, Apr 16 2023
%Y Cf. A053000, A107819.
%K nonn
%O 1,2
%A _Angad Singh_, Apr 11 2023