A360061 - OEIS

%I #37 Feb 03 2025 09:37:03

%S 2,3,4,12,48,54,66,138,144,162,168,180,198,234,252,264,330,360,366,

%T 372,402,420,444,462,480,534,546,552,564,576,600,630,642,678,702,744,

%U 756,846,852,858,882,966,1008,1206,1242,1254,1266,1272,1296,1302,1338,1650

%N Lexicographically earliest increasing sequence such that a(1) = 2 and for n >= 2, a(1)^2 + a(2)^2 + ... + a(n)^2 is a prime.

%e For n >= 2, partial sums of squares are (showing primality): 2^2 + 3^2 = 13; 13 + 4^2 = 29; 29 + 12^2 = 173; 173 + 48^2 = 2477; ...

%p s:= proc(n) option remember; `if`(n<1, 0, a(n)^2+s(n-1)) end:

%p a:= proc(n) option remember; local k, m;

%p       k:= s(n-1); for m from 1+a(n-1)

%p       while not isprime(k+m^2) do od; m

%p     end: a(1):=2:

%p seq(a(n), n=1..52);  # _Alois P. Heinz_, Jan 26 2023

%t s[n_] := s[n] = If[n < 1, 0, a[n]^2 + s[n-1]];

%t a[n_] := a[n] = Module[{k, m},

%t    k = s[n-1]; For[m = 1 + a[n-1],

%t    !PrimeQ[k + m^2], m++]; m];

%t a[1] = 2;

%t Table[a[n], {n, 1, 52}] (* _Jean-François Alcover_, Feb 03 2025, after _Alois P. Heinz_ *)

%o (Haskell)

%o import Math.NumberTheory.Primes.Testing (isPrime)

%o a360061_list = 2 : 3 : recurse 4 13 where

%o   recurse n p

%o     | isPrime(n^2 + p) = n : recurse (n+1) (n^2 + p)

%o     | otherwise        = recurse (n+1) p

%o -- _Peter Kagey_, Jan 25 2023

%Y Cf. A051935, A137326.

%K easy,nonn

%O 1,1

%A _Win Wang_, Jan 23 2023