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.
%I A174167 #13 Mar 02 2018 02:13:46 %S A174167 2,2,1,3,1,3,2,4,4,2,7,4,1,6,3,10,1,10,6,2,10,5,12,9,9,4,6,3,9,26,6, %T A174167 10,5,18,4,17,11,10,17,13,3,23,3,9,6,36,32,8,6,9,15,10,22,19,18,15,7, %U A174167 22,15,9,31,43,13,6,14,47,25,35,10,10,21,32,23,18,9,27,34,18,32,46,3,38,12,20 %N A174167 Number of safe primes between squares of consecutive primes. %C A174167 If you graph n vs a(n), interesting patterns begin to emerge. As you go farther along the n-axis, greater are the number of Safe Primes, on average, within each interval obtained. The smallest count of 1 occurs 4 times (terms: 3rd, 5th, 13th, and 17th) in the sequence above. I suspect the number of Safe Primes within each interval will never be zero. If one could prove this, then it would imply that Safe Primes are infinite. Can you prove it? %H A174167 Jaspal Singh Cheema, <a href="/A174167/b174167.txt">Table of n, a(n) for n = 1..10177</a> %H A174167 Rick Aster, <a href="http://www.globalstatements.com/shortcuts/88a.html"> Prime number sieve</a>, SAS prime sieve program %H A174167 Wikipedia, <a href="http://en.wikipedia.org/wiki/Safe_prime">Safe prime</a> %e A174167 Take any pair of consecutive primes. Let us say the very first one (2,3). Square both terms to obtain an interval (4,9). Within this interval, there are two Safe Primes, namely 5 and 7. Hence the very first term of the sequence above is 2. Similarly, the next term, 2, refers to the two Safe Primes between squares of (3,5), or the interval (9,25), which are 11 and 23. %Y A174167 Cf. A005385, A156875. %K A174167 nonn %O A174167 1,1 %A A174167 _Jaspal Singh Cheema_, Mar 10 2010 %E A174167 Edited by _D. S. McNeil_, Nov 17 2010