COMMENTS
If p is Cuban a cuban prime (A002407) and p == 3 (mod 4) (A002145), then m = 3*p is a term. Indeed, there is k for which p = 1 + 3*k*(k + 1) and m = 3*p = 3 + 9*k*(k + 1) = (3*k + 2)^2 - (3*k + 2) + 1, so m is a term.
Discussion
Sat Apr 06
15:51
Jon E. Schoenfield: (For the use of the spelling “cuban prime” [rather than “Cuban prime”] — a term which was derived from “cube” [rather than from “Cuba”] — see A002407, especially the term’s spelling in that sequence entry’s Comments section and in the articles at the last two entries in its Links section.)
COMMENTS
The sequence also includes terms that do not have this form: 133 = 12^2 - 12 + 1 = 7*19, 553 = 24^2 - 24 + 1 = 7*79, 1057 = 33^2 - 33 + 1 = 7 * 151, 1333 = 37^2 - 37 + 1= 31*43 and others.
COMMENTS
The sequence also includes terms that do not have this form: 133 = 12^2 - 12 + 1 = 7*19, 553 = 24^2 - 24 + 1 = 7*79, 1057 = 33^2 - 33 + 1 = 7 * 151, 1333 = 37^2 - 37 + 1= 31*43 and others.
Discussion
Sun Mar 24
07:39
Marius A. Burtea: Working with numbers of the form n^2 - n + 1 (A002061), we noticed that (3k + 2)^2 -(3k + 2) + 1= 9k^2 + 9k + 3 = 3*(3k^2 + 3k + 1), where 3k^2 + 3k + 1 = (k + 1)^3 - k^3, (A003215). I also saw that 3k^2 + 3k + 1 = 1 + 3*k*(k + 1) and I looked for primes of the form p = 1+3*k*(k+1) and found A002407. The association 9k^2 + 9k + 3 = 3*p led me to semiprime numbers, particularly Blum numbers.
Sun Mar 31
08:38
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Discussion
Sun Mar 24
00:06
Robert Munafo: The comment would be easier for me to follow if rearranged thusly:
Some terms are 3*A002407(i), specifically when p is a cuban prime of the form 3*k*(k+1)+1 for some k, because then 3*p = 9*k*(k+1)+3 = (3*k+2)^2 - (3*k+2) + 1 = A002061(3*k+2); and the two primes satisfying membership in A016105 are 3 and p. But this sequence also includes terms not of this form, the first being 133=12^2-12+1=7*19.
More importantly I think this needs some indication of what question or investigation led to the sequence's discovery (and/or invention)
Discussion
Wed Feb 28
02:15
Michel Marcus: Intersection of
