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Numbers that are both octagonal numbers (A000567) and octagonal pyramidal numbers (A002414).
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%I #34 Dec 21 2024 01:00:41

%S 0,1,1045,5985,123395663059845,774611255177760

%N Numbers that are both octagonal numbers (A000567) and octagonal pyramidal numbers (A002414).

%C Terms correspond to integral points on an elliptic curve, which allows all of them to be found efficiently. - _Max Alekseyev_, Feb 19 2024

%o (PARI) for(k=0, 1e5, if(ispolygonal(m=k*(k+1)*(2*k-1)/2, 8), print1(m", ")))

%Y Intersection of A000567 and A002414.

%Y Cf. A027568, A334012.

%Y Cf. A378361 (octagonal indices), A378918 (octagonal pyramidal indices).

%K nonn,fini,full

%O 1,3

%A _Seiichi Manyama_, May 16 2021

%E Keywords 'fini' and 'full' added by _Max Alekseyev_, Feb 19 2024