Question

2 starting terms of a diginacci sequence when the 2021st term is 11

Answer 1

Hello,

In a diginacci sequence, all term is the sum off digits of the 2 terms before.

Answer: 2,3

`u_(-2)=1\\u_(-1)=1\\u_0=digit(u_(-2))+digit(u_(-1))=1+1=2\\u_1=1+2=3\\u_2=2+3=5\\u_3=3+5=8\\u_4=5+8=13\\u_5=8+1+3=12\\...\\u_(18)=11\\u_(19)=8\\u_(20)=10\\u_(21)=9\\u_(22)=10\\u_(23)=10\\u_(24)=2**********\\u_(25)=3**********\\2020=24*84+4\\u_(2020)=u_(4)=13\\`

We must begin with 13 , 10

Proof:

Dim a As Long, b As Long, c As Long, nb As Integer

a = 13

b = 10

nb = 1

Print nb, a

While nb < 2021

nb = nb + 1

c = somme&(a, b)

a = b

b = c

' Print nb, a

Wend

Print nb, a

End

Function somme& (a1 As Long, b1 As Long)

Dim strA As String, strB As String, n As Long

strA = LTrim$(Str$(a1))

strB = LTrim$(Str$(b1))

n = 0

For i = 1 To Len(strA)

n = n + Val(Mid$(strA, i, 1))

Next i

For i = 1 To Len(strB)

n = n + Val(Mid$(strB, i, 1))

Next i

somme& = n

End Function