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 A214036 Numbers n such that floor(sqrt(1)) + floor(sqrt(2)) + floor(sqrt(3)) + ... + floor(sqrt(n)) is prime. 1
 2, 3, 4, 5, 7, 8, 10, 14, 36, 37, 39, 42, 43, 44, 46, 47 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is complete. Indeed, let s(n) be the sum of floor(sqrt(k)) for k from 1 to n. It is easy to verify that s(n^2+j), for 0 <= j < (n+1)^2-n^2, is equal to n(j+1) + n(4n+1)(n-1)/6, which is always divisible by n or by n/6 for n > 6. - Giovanni Resta, Mar 26 2014 LINKS EXAMPLE 2 is a term because floor(sqrt(1))+floor(sqrt(2)) = 1+1 = 2 is prime; 14 is a term because floor(sqrt(1))+ ... +floor(sqrt(14)) = 1+1+1+2+2+2+2+2+3+3+3+3+3+3 = 31 is prime. MAPLE A214036:=proc(q)  local a, n; a:=0; for n from 1 to q do a:=a+floor(sqrt(n)); if isprime(a) then print(n); fi; od; end: A214036(10^10); Alternative program: A214036_bis:=proc(q)  local a, j, n; a:=0; for n from 1 to q do for j from 1 to 2*n+1 do     a:=a+n; if isprime(a) then print(n^2+j-1); fi; od; od; end: A214036_bis(10^10); MATHEMATICA Position[Accumulate[Table[Floor[Sqrt[n]], {n, 50}]], _?PrimeQ]//Flatten (* Harvey P. Dale, Apr 14 2017 *) PROG (PARI) default(realprecision, 66); sm = 0; /* sum(n>=1, floor(sqrt(n)) */ for (n=1, 10^9, sm+=sqrtint(n); if (isprime(sm), print1(n, ", "))); /* Joerg Arndt, Mar 07 2013 */ CROSSREFS Cf. A220953. Sequence in context: A339279 A034296 A075745 * A100289 A255130 A054021 Adjacent sequences:  A214033 A214034 A214035 * A214037 A214038 A214039 KEYWORD nonn,fini,full AUTHOR Paolo P. Lava, Mar 06 2013 STATUS approved

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)