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A248580 a(n) = the smallest triangular number T(k) such that n*T(k)-1 and n*T(k)+1 are twin primes or 0 if no solution exists for n; T(k) = A000217(k) = k-th triangular number. 2
6, 3, 6, 1, 6, 1, 6, 0, 0, 3, 78, 1, 66, 3, 10, 15, 6, 1, 78, 3, 300, 21, 6, 3, 6, 78, 10, 15, 210, 1, 378, 6, 6, 3, 66, 3, 1596, 6, 28, 6, 528, 1, 990, 15, 6, 3, 6, 66, 78, 3, 28, 6, 120, 15, 210, 105, 10, 6, 528, 1, 378, 21, 36, 3, 36, 3, 66, 15, 28, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For n = 8 and 9 there are no triangular numbers T(k) such that n*T(k)-+1 are twin primes.
a(8) = 0 because 8*T(k)+1 = A016754(k) = composite number for k >= 1.
a(9) = 0 because 9*T(k)+1 = A060544(k+1) = composite number for k >= 1.
Are there numbers n > 9 such that a(n) = 0? If a(n) = 0 for n > 9, n must be bigger than 4000.
LINKS
FORMULA
a(n) = A000217(A248579(n)).
EXAMPLE
a(5) = 6 because 6 is the smallest smallest triangular number with this property: 5*6 -+ 1 = 29 and 31 (twin primes).
MATHEMATICA
a248580[n_Integer] := Catch@Module[{T, k}, T[i_] := i (i + 1)/2; Do[If[And[PrimeQ[n*T[k] + 1], PrimeQ[n*T[k] - 1]], Throw[T[k]], 0], {k, 1, 10^4}] /. Null -> 0]; a248580 /@ Range[70] (* Michael De Vlieger, Nov 12 2014 *)
PROG
(Magma) A248580:=func<n|exists(r){m*(m+1)/2:m in[1..1000000] | IsPrime(n*m*(m+1) div 2+1) and IsPrime(n*m*(m+1) div 2-1)}select r else 0>; [A248580(n): n in[1..100]]
(PARI) a(n) = {if ((n==8) || (n==9), return (0)); k = 1; while (!isprime(n*k*(k+1)/2-1) || !isprime(n*k*(k+1)/2+1), k++); k*(k+1)/2; } \\ Michel Marcus, Nov 12 2014
CROSSREFS
Sequence in context: A019151 A367976 A143506 * A008567 A233700 A195436
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Oct 25 2014
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)