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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 18 17:57 EST 2014. Contains 252173 sequences.