A361741 Starting positions of digit triples in the decimal expansion of Pi where the sum of the first 2 equals the third.

1, 3, 10, 29, 61, 73, 83, 106, 117, 132, 177, 192, 195, 198, 241, 248, 251, 281, 309, 311, 333, 362, 381, 393, 432, 477, 486, 494, 504, 508, 525, 532, 536, 555, 602, 611, 628, 647, 662, 674, 689, 699, 710, 747, 755, 760, 771, 806, 853, 856, 887, 899, 927, 934, 966, 969, 989

Offset

1,2

Comments

The first digit of Pi, "3", is reckoned as position 1.

This pattern happens from the first digit of Pi, so it seems to be pretty basic.

Links

Table of n, a(n) for n=1..57.

Index entries for sequences related to the number Pi

Formula

Integers k such that A000796(k) + A000796(k+1) = A000796(k+2).

Equivalently, A110883(k) = A000796(k+2).

In a random model of this sequence (call it A(n)), A(n) ~ kn with probability 1, where k = 200/11. - Charles R Greathouse IV, Mar 28 2023

Example

1 is the first term, since the first two digits 3 and 1 add up to 4.
3 is the second term, since 4 + 1 = 5.
10 is next, since 3 + 5 = 8.

Prog

(MATLAB)
p=char(vpa(pi, 1000)); p(2)='3';
for i=2:strlength(p)-2
  if str2num(p(i))+str2num(p(i+1))==str2num(p(i+2)) fprintf('%i, ', i-1)  end
end

Crossrefs

Cf. A000796, A110883.

Sequence in context: A260811 A108912 A350821 * A055336 A092325 A130218

Adjacent sequences: A361738 A361739 A361740 * A361742 A361743 A361744

Keyword

nonn,base

Author

Aaron T Cowan, Mar 22 2023

Status

approved