Jacobsthal numbers: Difference between revisions
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=={{header|AutoHotkey}}==
<lang AutoHotkey>Jacobsthal(n){
return SubStr(" " Format("{:.0f}", (2**n - (-1)**n ) / 3), -8)
}
Jacobsthal_Lucas(n){
return SubStr(" " Format("{:.0f}", 2**n + (-1)**n), -8)
}
prime_numbers(n) {
if (n <= 3)
return [n]
ans := [], done := false
while !done {
if !Mod(n,2)
ans.push(2), n /= 2
else if !Mod(n,3)
ans.push(3), n /= 3
else if (n = 1)
return ans
else {
sr := sqrt(n), done := true, i := 6
while (i <= sr+6) {
if !Mod(n, i-1) { ; is n divisible by i-1?
ans.push(i-1), n /= i-1, done := false
break
}
if !Mod(n, i+1) { ; is n divisible by i+1?
ans.push(i+1), n /= i+1, done := false
break
}
i += 6
}}}
ans.push(n)
return ans
}</lang>
Examples:<lang AutoHotkey>result := "First 30 Jacobsthal numbers:`n"
loop 30
result .= Jacobsthal(A_Index-1) (mod(A_Index, 5) ? " ":"`n")
result .= "`nFirst 30 Jacobsthal-Lucas numbers:`n"
loop 30
result .= Jacobsthal_Lucas(A_Index-1) (mod(A_Index, 5) ? " ":"`n")
result .= "`nFirst 20 Jacobsthal oblong numbers:`n"
loop 20
result .= SubStr(" " Jacobsthal(A_Index-1) * Jacobsthal(A_Index), -8) (mod(A_Index, 5) ? " ":"`n")
result .= "`nFirst 10 Jacobsthal primes:`n"
c:=0
while c < 10
if (prime_numbers(x:=Jacobsthal(A_Index)).Count() = 1 && x > 1)
result .= x (mod(++c, 5) ? " ":"`n")
MsgBox, 262144, , % result
return</lang>
{{out}}
<pre>First 30 Jacobsthal numbers:
0 1 1 3 5
11 21 43 85 171
341 683 1365 2731 5461
10923 21845 43691 87381 174763
349525 699051 1398101 2796203 5592405
11184811 22369621 44739243 89478485 178956971
First 30 Jacobsthal-Lucas numbers:
2 1 5 7 17
31 65 127 257 511
1025 2047 4097 8191 16385
32767 65537 131071 262145 524287
1048577 2097151 4194305 8388607 16777217
33554431 67108865 134217727 268435457 536870911
First 20 Jacobsthal oblong numbers:
0 1 3 15 55
231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503
238612935 954429895 817763271 270965703 084037575
First 10 Jacobsthal primes:
3 5 11 43 683
2731 43691 174763 2796203 715827883</pre>
=={{header|C}}==
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