

A110557


Shadow of sqrt(2).


1



1, 15, 157, 170, 175, 181, 183, 186, 193, 223, 232, 282, 286, 294, 374, 390, 478, 550, 970, 1066, 2046, 2124, 2180, 3147, 3165, 3240, 3277, 3346, 3826, 3899, 3916, 3982, 4061, 4798, 5788, 6520, 6567, 6651, 6713, 6723, 6793, 6831, 7681, 8068, 8121, 8164
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OFFSET

1,2


COMMENTS

First differences are sqrt(2)'s shadow. Never twice the same integer in sequence or first differences.


LINKS

Table of n, a(n) for n=1..46.


EXAMPLE

The first line below is the sequence, the second gives the first differences:
1..15...157..170.175.181.183.186.193..223.232..282.286.294
.14..142...13...5...6...2...3...7...30...9...50...4...8 < sqrt(2) shadow
sqrt(2) = 1.4142135623730950488016887242096980785696718753769...


MATHEMATICA

a[1] = 1; a[n_] := a[n] = Block[{c = RealDigits[ Sqrt[2], 10, 300][[1]], k = 1, t = Table[a[i], {i, n  1}]}, d = Drop[t, 1]  Drop[t, 1]; b = Drop[c, Length[ Flatten[ IntegerDigits /@ d]]]; e = Union[ Join[t, d]]; While[f = FromDigits[ Take[b, k]]; Position[e, f] != {}  b[[k + 1]] == 0, k++ ]; f + a[n  1]]; Table[ a[n], {n, 46}] (* Robert G. Wilson v *)


CROSSREFS

Cf. A002193.
Sequence in context: A223995 A006096 A099915 * A016304 A016849 A232414
Adjacent sequences: A110554 A110555 A110556 * A110558 A110559 A110560


KEYWORD

easy,nonn,base


AUTHOR

Eric Angelini and Alexandre Wajnberg, Sep 14 2005


EXTENSIONS

More terms from Robert G. Wilson v, Oct 10 2005


STATUS

approved



