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 A348019 Decimal expansion of Sum_{k>=1} prime(k)/10^(2^k). 0
 2, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET -1,1 COMMENTS This constant appears in a formula derived by Sierpiński (1952) that generates all the prime numbers. As in the case of other formulas for calculating prime numbers, this formula is not practical: for calculating the k-th prime one has to calculate the first k primes in order to get the constant with enough accuracy. REFERENCES Ralph G. Archibald, An introduction to the theory of numbers, Merrill, 1970, p. 282. Raymond Ayoub, An introduction to the analytic theory of numbers, AMS, 1963, p. 129. Paulo Ribenboim, The New Book of Prime Number Records, Springer, 1996, p. 182. LINKS Table of n, a(n) for n=-1..85. Chris K. Caldwell, FAQ: Is there a formula for the nth Prime?, The PrimePages. Paul Pollack, Not Always Buried Deep: A Second Course in Elementary Number Theory, AMS, 2009, p. 13. Andrzej Rotkiewicz, W. Sierpiński’s works on the Theory of Numbers, Rend. Circ. Mat. Palermo, Vol. 21 (1972), pp. 5-24. Wacław Sierpiński, Sur une formule donnant tous les nombres premiers, Comptes rendus hebdomadaires des séances de l'Académie des sciences, Vol. 235, No. 19 (1952), pp. 1078-1079; alternative link. FORMULA prime(n) = floor(c * 10^(2^n)) - 10^(2^(n-1)) * floor(c * 10^(2^(n-1))), where c is this constant (Sierpiński, 1952). EXAMPLE 0.02030005000000070000000000000011000000000000000000... MATHEMATICA RealDigits[Sum[Prime[i]/10^(2^i), {i, 1, 7}]][[1]] CROSSREFS Similar constants: A051021, A079614, A086238, A300753. Sequence in context: A348223 A035199 A035229 * A285982 A261727 A234579 Adjacent sequences: A348016 A348017 A348018 * A348020 A348021 A348022 KEYWORD nonn,cons,easy AUTHOR Amiram Eldar, Sep 24 2021 STATUS approved

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Last modified September 8 07:54 EDT 2024. Contains 375751 sequences. (Running on oeis4.)