A112677 - OEIS

%I #17 Feb 10 2019 03:41:14

%S 1,1,1,1,4,7,4,7,4,4,10,7,7,10,7,4,10,4,7,7,10,10,7,7,7,4,7,7,7,7,10,

%T 4,10,4,10,10,7,4,4,7,4,10,7,10,4,4,7,7,4,4,4,10,4,4,4,4,7,10,7,10,7,

%U 7,4,10,10,4,10,7,4,7,10,10,4,4,10,10,10,7,10,10,10,10

%N Sum of digits of the sum of the previous 4 terms.

%C This is to the tetranacci sequence as A112661 is to the tribonacci and as A030132 is to Fibonacci. A000288 is the tetranacci sequence (A000078) but starting with values (1,1,1,1). Andrew Carmichael Post (andrewpost(AT)gmail.com) wrote the program that generated this sequence and showed that for any 4 initial integers a(0),a(1),a(2),a(3) the length of the cycle eventually entered is a factor of 312. For instance, starting with (6,6,6,6) continues in a cycle of length 1 since SOD(6+6+6+6) = SOD(24) = 6; and 1 divides 312. For the SOD(tribonacci) which is A112661, the length of any cycle eventually entered is a factor of 78.

%C All terms for n >= 4 are 4, 7, or 10. The sequence has period 78; the 78 terms after the initial 1,1,1,1 repeat forever. - _Nathaniel Johnston_, May 04 2011

%F a(0)=a(1)=a(2)=a(3)=1. a(n) = SumDigits(a(n-1) + a(n-2) + a(n-3) + a(n-4)).

%F a(n) = SumDigits(A000288(n)).

%F a(n) = A007953(a(n-1) + a(n-2) + a(n-3) + a(n-4)). - _Nathaniel Johnston_, May 04 2011

%e a(0)=a(1)=a(2)=a(3)=1.

%e a(4) = SOD(1+1+1+1) = SOD(4) = 4.

%e a(5) = SOD(1+1+1+4) = SOD(7) = 7.

%e a(10) = SOD(4+7+4+4) = SOD(19) = 10, note that we do not iterate SOD to reduce 10 to 1.

%p A112677 := proc(n) option remember: if(n<=3)then return 1:fi: return add(d,d=convert(procname(n-1) + procname(n-2) + procname(n-3) + procname(n-4),base,10)): end: seq(A112677(n),n=0..100); # _Nathaniel Johnston_, May 04 2011

%t nxt[{a_,b_,c_,d_}]:={b,c,d,Total[IntegerDigits[a+b+c+d]]}; Transpose[ NestList[ nxt,{1,1,1,1},90]][[1]] (* or *) PadRight[{1,1,1,1},120,{10,10,10,10,4,7,4,7,4,4,10,7,7,10,7,4,10,4,7,7,10,10,7,7,7,4,7,7,7,7,10,4,10,4,10,10,7,4,4,7,4,10,7,10,4,4,7,7,4,4,4,10,4,4,4,4,7,10,7,10,7,7,4,10,10,4,10,7,4,7,10,10,4,4,10,10,10,7}](* _Harvey P. Dale_, Mar 05 2016 *)

%Y Cf. A000078, A000288, A004090, A007953, A010888, A030132, A112661.

%K base,easy,nonn

%O 0,5

%A _Jonathan Vos Post_, Dec 30 2005

%E Name corrected by _Nathaniel Johnston_, May 04 2011