A110557 - OEIS

A110557

Shadow of sqrt(2).

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

G. C. Greubel, Table of n, a(n) for n = 1..5000

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, Oct 10 2005 *)

CROSSREFS

Cf. A002193.

Sequence in context: A346843 A341918 A099915 * A016304 A016849 A300077

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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