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

Author

Aaron T Cowan, Mar 22 2023

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Index entries for sequences related to the number Pi

Crossrefs

Cf. A000796, A110883.

Programs

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

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