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A056895
If the smallest prime with a square excess of n is p then a(n)^2 = p - n.
3
1, 1, 2, 3, 6, 5, 4, 9, 8, 7, 6, 7, 10, 15, 8, 9, 24, 11, 12, 21, 16, 13, 12, 13, 16, 15, 14, 17, 18, 31, 20, 27, 20, 23, 18, 19, 22, 21, 20, 23, 24, 23, 24, 27, 28, 29, 30, 25, 38, 39, 26, 31, 30, 35, 28, 45, 34, 31, 42, 31, 34, 33, 32, 33, 36, 35, 34, 75, 40, 37, 36, 41, 48, 45
OFFSET
1,3
LINKS
FORMULA
a(n) = sqrt(A056893(n)-n) = A000196(A056893(n)) = sqrt(A056894(n)).
EXAMPLE
a(4)=3 because the smallest prime with a square excess of 4 is 13 and 13 - 4 = 3^2.
MATHEMATICA
a = {}; Do[p = 2; While[n != p - (r = Floor@Sqrt[p])^2, p = NextPrime[p]]; AppendTo[a, r], {n, 74}]; a (* Ivan Neretin, May 02 2019 *)
PROG
(PARI) a(n) = {my(p=2); while(n != p-sqrtint(p)^2, p = nextprime(p+1)); sqrtint(p - n); } \\ Michel Marcus, May 05 2019
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jul 05 2000
STATUS
approved