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A076818
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Lexicographically earliest sequence of pairwise coprime tetrahedral numbers.
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2
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1, 4, 35, 969, 302621, 437989, 657359, 939929, 3737581, 6435689, 9290431, 21084251, 26536591, 39338069, 44101441, 61690919, 112805879, 289442201, 439918931, 1008077071, 1103914379, 1220664491, 1369657969, 1504148881, 1779510701, 1868223839, 2252547431
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OFFSET
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1,2
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COMMENTS
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Previous name was: Tetrahedral numbers ((k^3-k)/6) which are coprime to each smaller number in this sequence.
Sierpinski proved that any finite set of pairwise coprime tetrahedral numbers can be extended by adding an additional tetrahedral number which is coprime with all the elements of the set. Therefore this sequence is infinite. - Amiram Eldar, Mar 01 2019
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REFERENCES
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W. Sierpiński, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970, Problem 43.
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LINKS
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EXAMPLE
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35 is a term because it is the least tetrahedral number after 4 which is coprime to 1 and 4.
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MATHEMATICA
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t[n_] := n (n + 1) (n +2)/6; s = {1}; While[Length[s] < 50, k = s[[-1]] + 1; While[Max[GCD[t[k], t /@ s]] > 1, k++]; AppendTo[s, k]]; t /@ s (* Amiram Eldar, Mar 01 2019 *)
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PROG
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(PARI) v=vector(1000); n=0; for(i=1, 540537, t=i*(i+1)*(i+2)/6; for(j=2, n, if(gcd(t, v[j])>1, next(2))); n++; v[n]=t); v \\ Donovan Johnson, Oct 10 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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