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A370519 Intersection of A002061 and A016105. 0
21, 57, 133, 381, 553, 813, 993, 1057, 1333, 1561, 1641, 1893, 1981, 2653, 2757, 3193, 3661, 5257, 5853, 6973, 8373, 8557, 9121, 9313, 10713, 10921, 12657, 13341, 15253, 15501, 16257, 18633, 19741, 22053, 24493, 29413, 30801, 32221, 32581, 33673, 35157, 39801 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If p is 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.
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.
LINKS
EXAMPLE
A002061(5) = 21 = A016105(1), so 21 is a term.
A002061(8) = 57 = A016105(3), so 57 is a term.
MATHEMATICA
TR=40000; R1=Ceiling[(1+Sqrt[1-4(1-TR)])/2]; R2=TR/4; Intersection[Table[n^2-n+1, {n, 0, R1}], Select[4Range[5, R2]+1, PrimeNu[#]==2&&MoebiusMu[#]==1&&Mod[FactorInteger[#][[1, 1]], 4]!=1&]](* James C. McMahon, Feb 27 2024 *)
PROG
(Magma) pd:=PrimeDivisors; blum:=func<n|#Divisors(n) eq 4 and #pd(n) eq 2 and pd(n)[1] mod 4 eq 3 and pd(n)[2] mod 4 eq 3>; [n:n in [s^2-s+1:s in [2..2000]]|blum(n)];
CROSSREFS
Sequence in context: A118057 A327902 A020148 * A037305 A370109 A223467
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Feb 27 2024
STATUS
approved

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Last modified July 21 06:08 EDT 2024. Contains 374463 sequences. (Running on oeis4.)