A058055 a(n) is the smallest positive number m such that m^2 + n is the next prime > m^2.
1, 3, 8, 5, 12, 11, 18, 51, 82, 49, 234, 23, 42, 75, 86, 231, 174, 107, 288, 63, 80, 69, 102, 325, 166, 765, 128, 143, 822, 727, 276, 597, 226, 835, 702, 461, 254, 693, 592, 797, 1284, 349, 370, 2337, 596, 645, 3012, 1033, 590, 4083, 1490, 757, 882, 833, 1668
Offset: 1
Keywords
Examples
n=6: a(6)=11 and 11^2+6 is 127, a prime; n=97: a(97) = 2144 and 2144^2+97 = 4596833, the least prime of the form m^2+97.
Links
- Zak Seidov, Table of n, a(n) for n = 1..500 (first 400 terms from T. D. Noe)
Programs
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Maple
for m from 1 to 10^5 do r:= nextprime(m^2)-m^2; if not assigned(R[r]) then R[r]:= m end if; end do: J:= map(op,{indices(R)}): N:= min({$1..J[-1]} minus J)-1: [seq(R[j],j=1..N)]; # Robert Israel, Aug 10 2012 -
Mathematica
nn = 100; t = Table[0, {nn}]; found = 0; m = 0; While[found < nn, m++; k = NextPrime[m^2] - m^2; If[k <= nn && t[[k]] == 0, t[[k]] = m; found++]]; t (* T. D. Noe, Aug 10 2012 *) -
Sage
R = {} # After Robert Israel's Maple script. for m in (1..2^12) : r = next_prime(m^2) - m^2 if r not in R : R[r] = m L = sorted(R.keys()) for i in (1..len(L)-1) : if L[i] != L[i-1]+1 : break [R[k] for k in (1..i)] # Peter Luschny, Aug 11 2012
Formula
a(n) = Min{ m > 0 | m^2 + n is the next prime after m^2}.
A053000(a(n)) = n. - Zak Seidov, Apr 12 2013
Extensions
Definition corrected by Zak Seidov, Mar 03 2008, and again by Franklin T. Adams-Watters, Aug 10 2012
Comments