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

1, 3, 4, 7, 12, 17, 18, 19, 20, 27, 28, 29, 30, 31, 32, 37, 42, 43, 48, 49, 50, 57, 58, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 93, 96, 97, 100, 103, 104, 105, 124, 133, 138, 147, 148, 153, 154, 163, 166, 171, 184, 193, 196, 197, 198, 205

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(2) = 3, since the smallest number greater than all the previous terms which gives a prime when added to 2^2 is 3.

Maple

R:= 1: t:= 1:
for n from 2 to 100 do
  t:= nextprime(t+n^2)-n^2;
  R:= R, t
od:
R; # Robert Israel, Apr 11 2023

Mathematica

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 *)

Prog

(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
(Python)
from sympy import nextprime
from itertools import count, islice
def agen(): # generator of terms
    an = 1
    for n in count(2):
        yield an
        an = nextprime(an + n**2) - n**2
print(list(islice(agen(), 62))) # Michael S. Branicky, Apr 16 2023

Crossrefs

Cf. A053000, A107819.

Sequence in context: A256726 A130324 A020677 * A310007 A158237 A389940

Adjacent sequences: A362219 A362220 A362221 * A362223 A362224 A362225

Keyword

nonn

Author

Angad Singh, Apr 11 2023

Status

approved