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
Keywords
Examples
a(2) = 3, since the smallest number greater than all the previous terms which gives a prime when added to 2^2 is 3.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Programs
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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
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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 *) -
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