Identificação de sequências numéricas na expansão decimal de π

#!/bin/bash

# Arkanon <[email protected]>
# 2025/06/05 (Thu) 04:26:45 -03
# 2025/06/05 (Thu) 02:30:17 -03

# <http://atractor.pt/mat/fromPI/PIsearch.html>


sudo apt-get install pi

time pi $((10**9)) > pi  # 67m9,650s

wc -c < pi               # 1000000002
sed "s/^..//" pi | wc -c # 1000000000

for i in F G E P; { time grep -o$i $s pi; }

dd if=pi bs=1c skip=2 count=10 2>&-; echo # 1415926535


pos()
{
  local n i s=${1?}
  time n=$(grep -oF $s pi | wc -l) # 11
  echo $n
  time for ((i=1;i<=n;i++))
  {
    sed "s/^..//;s/$s/\n/$i" pi |
    LC_NUMERIC=pt_BR.utf8 awk '{printf "%'\''11i\n", 1+length}' |
    head -n1
  } | nl -w3 -s'  '
}


check()
{
  local pos=${1?} len=${2?}
  dd if=pi bs=1c skip=$((2+${pos//.}-1)) count=$len 2>&-; echo
}


# <http://fb.com/bbcnewsbrasil/videos/718526187341534/?comment_id=1219544899384535>

pos 06111982 8
#  1  132.441.625
#  2  140.362.410
#  3  165.026.204
#  4  231.707.620
#  5  523.214.813
#  6  544.500.848
#  7  670.248.601
#  8  692.815.027
#  9  847.186.872
# 10  906.621.305
# 11  907.622.927
#
# 0m03,718s
# 1m24,856s

check 907.622.927 8

pos 19821106
#  1   40.586.516
#  2   45.463.015
#  3  255.076.215
#  4  282.922.620
#  5  327.418.957
#  6  410.776.841
#  7  516.909.942
#  8  581.766.209
#  9  604.401.827
# 10  806.850.982
# 11  846.107.576
# 12  908.604.255
#
# 0m02,779s
# 1m28,778s


# <http://fb.com/bbcnewsbrasil/videos/718526187341534/?comment_id=9801557443245986>

pos 20021986
#  1   29.458.308
#  2  125.210.989
#  3  193.439.009
#  4  199.246.089
#  5  236.427.252
#  6  509.117.561
#  7  520.446.597
#  8  629.973.436
#  9  721.062.016
# 10  732.115.060
# 11  745.321.152
# 12  754.075.841
# 13  821.453.254
# 14  918.890.445
# 15  935.662.384
# 16  962.787.711
#
# 0m02,869s
# 2m07,777s

check 199.246.089

pos 19860220
#  1   14.455.109
#  2   57.871.929
#  3   83.133.937
#  4  122.586.287
#  5  242.974.880
#  6  443.154.654
#  7  482.601.851
#  8  483.049.239
#  9  664.132.876
# 10  821.019.387
# 11  861.891.996
#
# 0m2,871s
# 1m15,337s