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Natural numbers with every odd prime p swapped with p+1.
4

%I #10 Nov 08 2016 07:45:49

%S 1,2,4,3,6,5,8,7,9,10,12,11,14,13,15,16,18,17,20,19,21,22,24,23,25,26,

%T 27,28,30,29,32,31,33,34,35,36,38,37,39,40,42,41,44,43,45,46,48,47,49,

%U 50,51,52,54,53,55,56,57,58,60,59,62,61,63,64,65,66,68,67,69,70,72,71

%N Natural numbers with every odd prime p swapped with p+1.

%H G. C. Greubel, <a href="/A135761/b135761.txt">Table of n, a(n) for n = 1..10000</a>

%e Start with sequence of positive integers, then swap a(i) and a(i+1) if a(i) is an odd prime:

%e a(1)=1, a(2)=2, then a(3)=4 and a(4)=3 because p=3 is odd prime and p and p+1 are swapped.

%p f:= proc(n) if isprime(2*n+1) then (2*n+2,2*n+1) else (2*n+1,2*n+2) fi end proc:

%p map(f, [$0..100]); # _Robert Israel_, Nov 07 2016

%t r=Range[100];Do[If[PrimeQ[r[[i]]],{r[[i]],r[[i+1]]}={r[[i+1]],r[[i]]}],{i,3,97,2}];r

%Y Cf. A135762.

%K nonn

%O 1,2

%A _Zak Seidov_, Nov 27 2007