# Sequences based on algorithms

Jonathan Post jvospost3 at gmail.com
Thu Nov 15 08:14:10 CET 2007

```I just submitted a related seq.  Whether the pattern I suggest for the
first 5 values (as subset of A132435) continues I leave to others,
perhaps through programming it, though I should have clicked "more" to
invite that.

%I A000001
%S A000001 6, 35, 143, 391, 899, 1739, 3233, 5293, 8051, 11413, 17653,
24883, 33389, 43931, 56977, 72731, 92881, 118829, 145699, 176039
%N A000001 Smallest prime between n^2 and (n+1)^2 times largest prime
between n^2 and (n+1)^2.
%C A000001 First 5 values are a subset of A132435. Subset of
semiprimes A001358. Suggested by Legendre's conjecture (still open)
that there is always a prime between n^2 and (n+1)^2.  A053001(n+1) -
A007491(n) = 1, 2, 2, 6, 2, 10, 8, 12, 14, 12, 12, 18, 20, 26, 24, 26,
24, 28, 30, 38, ... not currently in OEIS.
%F A000001 a(n) = A007491(n) * A053001(n+1).
%e A000001 a(1) = 6 = 2*3 = (smallest prime in [1^2,2^2]) * (largest
prime in [1^2,2^2]).
a(2) = 35 = 5*7 = (smallest prime in [2^2,3^2]) * (largest prime in [2^2,3^2]).
a(3) = 143 = 11*13 = (smallest prime in [2^2,3^2]) * (largest prime in
[2^2,3^2]).
a(4) = 391 = 17*23 = (smallest prime in [3^2,4^2]) * (largest prime in
[3^2,4^2]).
%Y A000001 Cf. A000040, A001358, A007491, A014085, A053000, A053001,
A053607, A077766, A077767, A132435.
%O A000001 1,1
%K A000001 ,easy,nonn,
%A A000001 Jonathan Vos Post (jvospost2 at yahoo.com), Nov 15 2007
RH
RA 192.20.225.32

```