cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A076818 Lexicographically earliest sequence of pairwise coprime tetrahedral numbers.

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%I A076818 #22 Mar 03 2019 04:00:59
%S A076818 1,4,35,969,302621,437989,657359,939929,3737581,6435689,9290431,
%T A076818 21084251,26536591,39338069,44101441,61690919,112805879,289442201,
%U A076818 439918931,1008077071,1103914379,1220664491,1369657969,1504148881,1779510701,1868223839,2252547431
%N A076818 Lexicographically earliest sequence of pairwise coprime tetrahedral numbers.
%C A076818 Previous name was: Tetrahedral numbers ((k^3-k)/6) which are coprime to each smaller number in this sequence.
%C A076818 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
%D A076818 W. SierpiƄski, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970, Problem 43.
%H A076818 Donovan Johnson, <a href="/A076818/b076818.txt">Table of n, a(n) for n = 1..1000</a>
%e A076818 35 is a term because it is the least tetrahedral number after 4 which is coprime to 1 and 4.
%t A076818 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 *)
%o A076818 (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
%Y A076818 Cf. A000292, A034792.
%K A076818 nonn
%O A076818 1,2
%A A076818 _Shyam Sunder Gupta_, Nov 19 2002
%E A076818 Edited by _Don Reble_, Nov 03 2005
%E A076818 New name from _Amiram Eldar_, Mar 02 2019