A248579 a(n) = the smallest numbers k such that n*T(k)-1 and n*T(k)+1 are twin primes or 0 if no solution exists for n where T(k) = A000217(k) = k-th triangular number.
3, 2, 3, 1, 3, 1, 3, 0, 0, 2, 12, 1, 11, 2, 4, 5, 3, 1, 12, 2, 24, 6, 3, 2, 3, 12, 4, 5, 20, 1, 27, 3, 3, 2, 11, 2, 56, 3, 7, 3, 32, 1, 44, 5, 3, 2, 3, 11, 12, 2, 7, 3, 15, 5, 20, 14, 4, 3, 32, 1, 27, 6, 8, 2, 8, 2, 11, 5, 7, 3, 167, 1, 20, 9, 12, 2, 3, 18
Offset: 1
Keywords
Examples
a(5) = 3 because 3 is the smallest number k with this property: 5*T(3) -/+ 1 = 5*6 -+ 1 = 29 and 31 (twin primes).
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Magma
A248579:=func
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Maple
f:= proc(n) local k; for k from 1 do if isprime(n*k*(k+1)/2+1) and isprime(n*k*(k+1)/2-1) then return k fi od: end proc; f(8):= 8: f(9):= 0: map(f, [$1..100]); # Robert Israel, Aug 10 2023
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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;} \\ Michel Marcus, Nov 05 2014
Comments