cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A132153 Largest prime <= square root of 10^n.

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%I A132153 #32 Mar 04 2025 13:08:47
%S A132153 3,7,31,97,313,997,3137,9973,31607,99991,316223,999983,3162277,
%T A132153 9999991,31622743,99999989,316227731,999999937,3162277633,9999999967,
%U A132153 31622776589,99999999977,316227766003,999999999989,3162277660153,9999999999971,31622776601657
%N A132153 Largest prime <= square root of 10^n.
%C A132153 To check if an (n+1)-digit number is prime, a(n) is the largest prime which one needs to check is not a factor of the (n+1)-th digit number. For example, to check that a general four-digit number is not prime, we need to test its divisibility by all the primes up to and including 97.
%H A132153 Charles R Greathouse IV, <a href="/A132153/b132153.txt">Table of n, a(n) for n = 1..2000</a>
%F A132153 a(n) = A000040(A122121(n)). a(2n) = A003618(n). - _R. J. Mathar_, Nov 06 2007 [Corrected by _Jaroslav Krizek_, Jul 12 2010]
%F A132153 a(n) = sqrt(A175734(n)). - _Jaroslav Krizek_, Aug 24 2010
%t A132153 Table[NextPrime[Sqrt[10^n],-1],{n,27}] (* _James C. McMahon_, Mar 04 2025 *)
%o A132153 (PARI) a(n)=precprime(sqrtint(10^n)) \\ _Charles R Greathouse IV_, Aug 18 2011
%o A132153 (Python)
%o A132153 from sympy import prevprime, integer_nthroot
%o A132153 def a(n): return prevprime(integer_nthroot(10**n, 2)[0]+1)
%o A132153 print([a(n) for n in range(1, 28)]) # _Michael S. Branicky_, Dec 23 2021
%Y A132153 Cf. A017934, A131581, A136582, A175733, A175734.
%Y A132153 Cf. A000040, A122121, A003618.
%K A132153 nonn
%O A132153 1,1
%A A132153 _Anthony C Robin_, Nov 01 2007
%E A132153 More terms from _N. J. A. Sloane_, Jan 05 2008