A172524 Partial sums of Iccanobif numbers A001129.

0, 1, 2, 4, 7, 12, 20, 33, 72, 196, 710, 1546, 2599, 6738, 19553, 80688, 185625, 978142, 2432840, 12112678, 29466988, 39202128, 40962878, 41948928, 42570288, 42684103, 43265540, 44518036, 52194742, 65214030, 159581828, 337649208

Offset

0,3

Comments

The only primes in this sequence are: 2, 7 and 19553. The squares in this sequence begin: 0, 1, 4, 196.

Links

Table of n, a(n) for n=0..31.

Formula

a(n) = SUM[i=0..n] A001129(i) = SUM[i=0..n] {a(0) = 0, a(1) = 1, a(i+2) = R(a(i)) + R(a(i+1))} = SUM[i=0..n] A001129(i) = SUM[i=1..n] {a(0) = 0, a(1) = 1, a(i+2) = A004086(a(i)) + A004086(a(i+1))}.

Example

a(14) = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 39 + 124 + 514 + 836 + 1053 + 4139 + 12815 = 19553 is prime. a(31) = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 39 + 124 + 514 + 836 + 1053 + 4139 + 12815 + 61135 + 104937 + 792517 + 1454698 + 9679838 + 17354310 + 9735140 + 1760750 + 986050 + 621360 + 113815 + 581437 + 1252496 + 7676706 + 13019288 + 94367798 + 178067380.

Mathematica

nxt[{a_, b_}]:={b, Total[FromDigits/@Reverse/@IntegerDigits[{a, b}]]}; Accumulate[ Transpose[NestList[nxt, {0, 1}, 40]][[1]]] (* Harvey P. Dale, Apr 04 2015 *)

Crossrefs

Cf. A000040, A000045, A001129, A004086, A014258-A014260.

Sequence in context: A093607 A005182 A329397 * A094925 A289168 A340217

Adjacent sequences: A172521 A172522 A172523 * A172525 A172526 A172527

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Feb 06 2010

Status

approved