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A228466
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Smallest odd number expressible in exactly n ways as p + 2*m^2 where p is 1 or a prime and m >= 0.
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1
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5777, 1, 3, 13, 19, 55, 61, 169, 139, 271, 181, 391, 439, 559, 661, 619, 829, 859, 1069, 1081, 1459, 1489, 1609, 1741, 1951, 2029, 2509, 2341, 3631, 3769, 3331, 3961, 4525, 4189, 4261, 5281, 4801, 6229, 6361, 5911, 6439, 7111, 6319, 13081, 9931, 8869, 10321
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OFFSET
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0,1
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LINKS
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EXAMPLE
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a(3) = 13 = 5+2*2^2 = 11+2*1^2 = 13+2*0^2. 13 is the smallest odd number expressible in exactly 3 ways.
a(4) = 19 = 1+2*3^2 = 11+2*2^2 = 17+2*1^2 = 19+2*0^2. 19 is the smallest odd number expressible in exactly 4 ways.
a(5) = 55 = 5+2*5^2 = 23+2*4^2 = 37+2*3^2 = 47+2*2^2 = 53+2*1^2. 55 is the smallest odd number expressible in exactly 5 ways.
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MATHEMATICA
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(* finds terms < mx *) upto[mx_] := Block[{r = Floor[1+mx/2], k, t, p, s = {}}, t = 0*Range@r; p = Prime@ Range@ PrimePi@ mx; p[[1]] = 1; t[[# + Range[0, Sqrt[r - #]]^2]]++ & /@ ((1 + p)/2); k = 0; While[(r = Position[t, k, 1, 1]) != {}, k++; AppendTo[s, 2 r[[1, 1]] - 1]]; s]; upto[10^5] (* Giovanni Resta, Aug 23 2013 *)
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PROG
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(PARI) /* finds terms up to a(1000) */ mx=10602619; v=vector(mx); nn=vector(1000); p=vector(701940); p[1]=1; pr=2; for(j=2, 701940, pr=nextprime(pr+1); p[j]=pr); for(m=0, 2302, m2=2*m^2; for(j=1, 701940, s=m2+p[j]; if(s<=mx, v[s]++, next(2)))); forstep(j=1, mx, 2, if(v[j]==0, write("b228466.txt", 0 " " j); j=mx)); forstep(j=1, mx, 2, if(v[j]>0, if(v[j]<=1000, if(nn[v[j]]==0, nn[v[j]]=j)))); for(n=1, 1000, write("b228466.txt", n " " nn[n]))
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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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