A229470 Positions of 2 in decimal expansion of 0.1231232331232332333..., whose definition is given below.

2, 5, 7, 11, 13, 16, 21, 23, 26, 30, 36, 38, 41, 45, 50, 57, 59, 62, 66, 71, 77, 85, 87, 90, 94, 99, 105, 112, 121, 123, 126, 130, 135, 141, 148, 156, 166, 168, 171, 175, 180, 186, 193, 201, 210, 221, 223, 226, 230, 235, 241, 248, 256, 265, 275, 287, 289, 292, 296, 301, 307, 314, 322, 331, 341, 352, 365, 367, 370, 374, 379, 385

Offset

1,1

Comments

0.1231232331232332333... = Sum_{k>=0} 10^(-(k + 3)! / (3! * k!)) * (1 + 10 * Sum_{l=2..k+2} 10^(-(l^2 + l) / 2) * ((10^l - 1) / 3 - 10^(l - 1))).

Links

Table of n, a(n) for n=1..72.

Formula

a((n^2+n+2m-2)/2) = (n^3+6n^2+3m^2+11n-3m+6)/6; n+2>=m>=2.

a(n) = Sum_{k=0..n-1} ( 1 + A002262(k) + A010054(k)*(sqrt(1+8*k)+1)/2 ).

Prog

(PARI) a(n)=sum(k=0, n-1, 1+k-binomial(round(sqrt(2+2*k)), 2)+issquare(8*k+1)*(sqrtint(1+8*k)+1)/2) /* Ralf Stephan, Oct 09 2013 */

Crossrefs

Sequence in context: A004134 A191406 A322969 * A157829 A020581 A081259

Adjacent sequences: A229467 A229468 A229469 * A229471 A229472 A229473

Keyword

easy,nonn,base,changed

Author

Jiri Klepl, Sep 24 2013

Extensions

Formula corrected by Ralf Stephan, Oct 09 2013

Status

approved