

A229470


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


0



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
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OFFSET

1,1


COMMENTS

0.1231232331232332333... = sum_{k=0..infinity, 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+2m2)/2) = (n^3+6n^2+3m^2+11n3m+6)/6; n+2>=m>=2.
a(n) = sum_(k=0..n1, 1 + A002262(k) + A010054(k)*(sqrt(1+8k)+1)/2 ).


PROG

(PARI) a(n)=sum(k=0, n1, 1+kbinomial(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


AUTHOR

Jiri Klepl, Sep 24 2013


EXTENSIONS

Formula corrected by Ralf Stephan, Oct 09 2013


STATUS

approved



