The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000006 Integer part of square root of n-th prime. (Formerly M0259 N0092) 22
 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Conjecture: No two successive terms in the sequence differ by more than 1. Proof of this would prove the converse of the theorem that every prime is surrounded by two consecutive squares, namely |sqrt(p)|^2 and (|sqrt(p)|+1)^2. - Cino Hilliard, Jan 22 2003 Equals the number of squares less than prime(n). Cf. A014689. - Zak Seidov Nov 04 2007 The above conjecture is Legendre's conjecture that for n > 0 there is always a prime between n^2 and (n+1)^2. See A014085, number of primes between two consecutive squares, which is also the number of times n is repeated in the present sequence. - Jean-Christophe Hervé, Oct 25 2013 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. Matthew Parker, The first 100 million terms (7-Zip compressed file) FORMULA a(n) = A000196(A000040(n)). - Reinhard Zumkeller, Mar 24 2012 MATHEMATICA a[n_] := IntegerPart[Sqrt[Prime[n]]] IntegerPart[Sqrt[#]]&/@Prime[Range] (* Harvey P. Dale, Mar 06 2012 *) PROG (PARI) (a(n)=sqrtint(prime(n))); vector(100, n, a(n)) \\ Edited by M. F. Hasler, Oct 19 2018 (PARI) apply(sqrtint, primes(100)) \\ Charles R Greathouse IV, Apr 26 2012 (PARI) apply( A000006=n->sqrtint(prime(n)), [1..100]) \\ M. F. Hasler, Oct 19 2018 (Haskell) a000006 = a000196 . a000040  -- Reinhard Zumkeller, Mar 24 2012 (Python) from sympy import sieve A000006 = lambda n: int(sieve[n]**.5) print([A000006(n) for n in range(1, 100+1)]) # Albert Lahat, Jun 25 2020 CROSSREFS Cf. A014085. See also A263846 (floor of cube root of prime(n)), A000196 (floor of sqrt(n)), A048766 (floor of cube root of n). Sequence in context: A024417 A060021 A350029 * A061017 A331535 A248170 Adjacent sequences:  A000003 A000004 A000005 * A000007 A000008 A000009 KEYWORD nonn,easy,nice AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 2 11:46 EDT 2022. Contains 357205 sequences. (Running on oeis4.)