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%I #6 Nov 27 2022 15:29:25
%S 2,5,6,8,9,26,27,28,71,72,73,487,488,489,490,491,492,493,494,495,496,
%T 497,498
%N Indices n where self-describing sequence A154328 has jumps, A154328(n) > A154328(n-1)+1.
%C The next term is on the order of 10^17, since the next constraint is A154328(27) = 10^19 = sum of the first 10^19 digits of A154328. Even if from term 500 on there were 30 digits "9" in each term, their sum would stay below 10^19 for more than 3*10^16 terms. But at index 498+10^12, the value of 10^31 is reached and among the next 10^17 terms, about half of the digits will be zero.
%e a(1)=2 since the 1st jump of A154328 occurs at index 2, where the value rises to A154328(2)=10 > A154328(1)+1=2.
%e a(2)=5 since the 2nd jump of A154328 occurs at index 5, where the value rises to A154328(5)=20 > A154328(4)+1=13.
%o (PARI) A154328={concat([[1,10,11,12,20,111,112,120], vector(16+1,i,-1+1000+i), 10000, 10^19, vector(42+1,i,-1+10^19+10^11*8+i), 10^19+4*10^18-1, 10^20-10^11+(10^11-1)/9, vector(413+1,i,-1+(10^21-10^16)/9+i), (10^21-10^16)/9+3*10^15-1, vector(10,i,10^(20+i)-1), 10^31-10^12 /* +i=0..10^17 */])};
%o for( i=2,#A154328, A154328[i] > A154328[i-1]+1 & print1(i","))
%Y A154330(n) = A154328(a(n)).
%K base,nonn
%O 1,1
%A _M. F. Hasler_, Jan 13 2009
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