A076818 Lexicographically earliest sequence of pairwise coprime tetrahedral numbers.

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

Offset: 1

Author

Shyam Sunder Gupta, Nov 19 2002

Keywords

• nonn

Comments

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

Examples

			35 is a term because it is the least tetrahedral number after 4 which is coprime to 1 and 4.
		

References

• W. Sierpiński, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970, Problem 43.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000292, A034792.

Programs

Mathematica

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 *)

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

Extensions

Edited by Don Reble, Nov 03 2005

New name from Amiram Eldar, Mar 02 2019