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A340221
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Constant whose decimal expansion is the concatenation of the smallest n-digit semiprime A098449(n), for n = 1, 2, 3, ...
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7
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4, 1, 0, 1, 0, 6, 1, 0, 0, 3, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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The terms of sequence A215647 converge to this sequence of digits, and to this constant, up to powers of 10.
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LINKS
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FORMULA
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c = 0.410106100310001100001100000110000001100000001100000000610000000003...
= Sum_{k >= 1} 10^(-k(k+1)/2)*A098449(k)
a(-n(n+1)/2) = 1 for all n >= 2, followed by increasingly more zeros.
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EXAMPLE
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The smallest prime with 1, 2, 3, 4, ... digits is, respectively, 2, 11, 101, 1009, .... Here we list the sequence of digits of these numbers: 2: 1, 1; 1, 0, 1; 1, 0, 0, 9; ...
This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.2111011009...
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PROG
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(PARI) concat([digits(A098449(k))|k<-[1..14]]) \\ as seq. of digits
c(N=20)=sum(k=1, N, .1^(k*(k+1)/2)*A098449(k)) \\ as constant
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CROSSREFS
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Cf. A098449 (smallest n-digit semiprime), A215647 (has this as "limit"), A340206 (same for squares, limit of A215689), A340207 (similar, with largest n-digit squares, limit of A339978), A340208 (same for cubes, limit of A215692), A340209 (same with largest n-digit cube, limit of A340115), A340219 (same for primes, limit of A215641).
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KEYWORD
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AUTHOR
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STATUS
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approved
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