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 A215689 Smallest prime whose decimal expansion consists of the concatenation of a 1-digit square, a 2-digit square, a 3-digit square, ..., and an n-digit square, or 0 if there is no such prime. 8
 0, 149, 125441, 1161002209, 116100102414161, 116100102410000106929, 1161001024100001004891442401, 116100102410000100489100000010169721, 116100102410000100489100000010004569100460529, 1161001024100001004891000000100045691000000001009269361 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The n-th term has n(n+1)/2 digits (cf. A000217). There are (0, 3, 29, 991, 175210, ...) primes of that form, for n = 1, 2, 3, .... We can conjecture that a(n) > 0 for all n, and even that the terms converge to the concatenation of (s(1), s(2), s(3), ...) where s(n) is the smallest n-digit square, cf. formula. - M. F. Hasler, Dec 31 2020 LINKS M. F. Hasler, Table of n, a(n) for n = 1..44 (all terms < 10^1000), Dec 31 2020. FORMULA a(n) ~ 10^(n(n+1)/2) * 0.1161001024100001004891000000100045691... - M. F. Hasler, Dec 31 2020 EXAMPLE a(2) = 149, which is a prime, and the concatenation of 1 = 1^2 with 49 = 7^2. a(3) = 125441, which is a prime, and the 1 = 1^2 with 25 = 5^2 with 441 = 21^2. PROG (PARI) apply( {A215689(n)=forvec(v=vector(n, k, [ceil(10^((k-1)/2)), sqrtint(10^k-1)]), ispseudoprime(n=eval(concat([Str(k^2)|k<-v])))&&return(n))}, [1..11]) \\ M. F. Hasler, Dec 31 2020 CROSSREFS Cf. A000040, A000290, A000217, A215641, A215647. Cf. A215692 (analog for cubes). Sequence in context: A188566 A188753 A188873 * A104262 A048706 A054729 Adjacent sequences:  A215686 A215687 A215688 * A215690 A215691 A215692 KEYWORD nonn,base AUTHOR Jonathan Vos Post, Aug 20 2012 EXTENSIONS More terms (up to a(10)) from Alois P. Heinz, Aug 21 2012 STATUS approved

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Last modified April 11 06:40 EDT 2021. Contains 342886 sequences. (Running on oeis4.)