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A202822
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Numbers of the form 3*(x^2 + xy + y^2 + x + y) + 1 where x and y are integers.
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10
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1, 4, 7, 13, 16, 19, 25, 28, 31, 37, 43, 49, 52, 61, 64, 67, 73, 76, 79, 91, 97, 100, 103, 109, 112, 121, 124, 127, 133, 139, 148, 151, 157, 163, 169, 172, 175, 181, 193, 196, 199, 208, 211, 217, 223, 229, 241, 244, 247, 256, 259, 268, 271, 277, 283, 289, 292
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OFFSET
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1,2
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COMMENTS
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Closed under multiplication.
Löschian numbers of the form 3*k+1. - Altug Alkan, Nov 18 2015
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LINKS
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FORMULA
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A033685(n) != 0 if and only if n is in the set.
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MATHEMATICA
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nf[{i_, j_}]:=3(i^2+i*j+j^2+i+j)+1; Union[nf/@Tuples[Range[-10, 10], 2]] (* Harvey P. Dale, Dec 31 2011 *)
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PROG
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(PARI) isA(n) = if(n%3 == 0, 0, 0 != sumdiv( n, d, kronecker( -3, d)))
(PARI) x='x+O('x^500); p=eta(x)^3/eta(x^3); for(n=0, 499, if(polcoeff(p, n) != 0 && n%3==1, print1(n, ", "))) \\ Altug Alkan, Nov 18 2015
(PARI) is(n)=(n%3==1) && #bnfisintnorm(bnfinit(z^2+z+1), n); \\ Joerg Arndt, Jan 04 2016
(PARI) list(lim)=my(v=List(), y, t); for(x=0, sqrtint(lim\3), my(y=x, t); while((t=x^2+x*y+y^2)<=lim, if((x-y)%3, listput(v, t)); y++)); Set(v) \\ Charles R Greathouse IV, Jul 05 2017
(Haskell)
a202822 n = a202822_list !! (n-1)
a202822_list = filter ((== 1) . flip mod 3) a003136_list
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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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