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A362222
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Slowest increasing sequence where a(n) + n^2 is a prime.
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1
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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a(2) = 3, since the smallest number greater than all the previous terms which gives a prime when added to 2^2 is 3.
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MAPLE
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R:= 1: t:= 1:
for n from 2 to 100 do
t:= nextprime(t+n^2)-n^2;
R:= R, t
od:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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