A280546 Index in A002193 of start of first occurrence of at least n consecutive equal digits in the decimal expansion of sqrt(2) after the decimal point.

2, 19, 150, 953, 2708, 32414, 158810, 4602784, 472173970, 472173970

Offset

1,1

Comments

We index the digits of sqrt(2) = 1.4142135... starting with 1 (for the 1), 2 (for the 4), 3 (for the second 1), 4 (for the second 4), 5 (for the 2), and so on.

Find the index of the first digit of a run of n consecutive equal digits after the decimal point: this is a(n). For example, the "88" here 1414213562373095048801.. begins at the 19th digit, so a(2) = 19. - N. J. A. Sloane, Mar 20 2023

Links

Table of n, a(n) for n=1..10.

Irrational Numbers Search Engine (searches initial 2 x 10^9 digits of sqrt(2))

Mathematica

Module[{nn=160000, s2}, s2=RealDigits[Sqrt[2], 10, nn][[1]]; Flatten[Table[ SequencePosition[ s2, PadRight[{}, k, x_], 1], {k, 7}], 1]][[;; , 1]] (* Harvey P. Dale, Mar 20 2023 *)

Prog

(PARI) string(n) = default(realprecision, n+10); my(x=sqrt(2)); floor(x*10^n)
digit(n) = string(n)-10*string(n-1)
searchstrpos(n) = my(x=1, i=1); while(1, my(y=x+1); while(digit(y)==digit(x), y++; i++); if(i >= n, return(x+1)); i=1; x++)
a(n) = searchstrpos(n)

Crossrefs

Cf. A002193, A244601, A277259, A277532.

Sequence in context: A166298 A220792 A220957 * A323141 A319962 A161608

Adjacent sequences: A280543 A280544 A280545 * A280547 A280548 A280549

Keyword

nonn,base,more

Author

Felix Fröhlich, Jan 05 2017

Status

approved