A300999 Add to a(n) the first digit of a(n+1) to get a(n+2), with a(1) = 1 and a(2) = 2.

1, 2, 3, 5, 8, 13, 9, 22, 11, 23, 13, 24, 15, 25, 17, 26, 19, 27, 21, 29, 23, 31, 26, 33, 29, 35, 32, 38, 35, 41, 39, 44, 43, 48, 47, 52, 52, 57, 57, 62, 63, 68, 69, 74, 76, 81, 84, 89, 92, 98, 101, 99, 110, 100, 111, 101, 112, 102, 113, 103, 114, 104, 115, 105, 116, 106, 117, 107, 118, 108, 119

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Mar 20 2018

Keywords

• nonn
• base
• easy

Comments

The sequence, starting with a(1) = 1 and a(2) = 2, never enters into a loop.

Examples

			a(1) + first digit of a(2) =  1 + 2 = a(3) =  3,
a(2) + first digit of a(3) =  2 + 3 = a(4) =  5,
a(3) + first digit of a(4) =  3 + 5 = a(5) =  8,
a(4) + first digit of a(5) =  5 + 8 = a(6) = 13,
a(5) + first digit of a(6) =  8 + 1 = a(7) =  9,
a(6) + first digit of a(7) = 13 + 9 = a(8) = 22,
a(7) + first digit of a(8) =  9 + 2 = a(9) = 11,
etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002

Crossrefs

Cf. A267809.

Programs

Mathematica

nxt[{a_,b_}]:={b,a+IntegerDigits[b][[1]]}; NestList[nxt,{1,2},80][[;;,1]] (* Harvey P. Dale, Nov 19 2023 *)

PARI

a=vector(10^4); a[1]=1; a[2]=2; for(n=3, #a, a[n]=digits(a[n-1])[1]+a[n-2]); a \\ Altug Alkan, Mar 20 2018