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Starting positions of digit triples in the decimal expansion of Pi where the sum of the first 2 equals the third.
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%I #66 May 02 2023 13:56:13

%S 1,3,10,29,61,73,83,106,117,132,177,192,195,198,241,248,251,281,309,

%T 311,333,362,381,393,432,477,486,494,504,508,525,532,536,555,602,611,

%U 628,647,662,674,689,699,710,747,755,760,771,806,853,856,887,899,927,934,966,969,989

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

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

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

%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>

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

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

%F 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

%e 1 is the first term, since the first two digits 3 and 1 add up to 4.

%e 3 is the second term, since 4 + 1 = 5.

%e 10 is next, since 3 + 5 = 8.

%o (MATLAB)

%o p=char(vpa(pi,1000));p(2)='3';

%o for i=2:strlength(p)-2

%o if str2num(p(i))+str2num(p(i+1))==str2num(p(i+2)) fprintf('%i,',i-1) end

%o end

%Y Cf. A000796, A110883.

%K nonn,base

%O 1,2

%A _Aaron T Cowan_, Mar 22 2023