cp's OEIS Frontend

A372292 Numbers that occur more than once in the odd bisection of A371094.

%I A372292 #13 Apr 26 2024 10:59:30
%S A372292 21,117,213,309,341,405,501,597,693,789,885,981,1077,1173,1269,1365,
%T A372292 1461,1557,1653,1749,1845,1877,1941,2037,2133,2229,2325,2421,2517,
%U A372292 2613,2709,2805,2901,2997,3093,3189,3285,3381,3413,3477,3573,3669,3765,3861,3957,4053,4149,4245,4341,4437,4533,4629,4725,4821,4917
%N A372292 Numbers that occur more than once in the odd bisection of A371094.
%C A372292 Numbers that occur more than once in array A371100.
%H A372292 Antti Karttunen, <a href="/A372292/b372292.txt">Table of n, a(n) for n = 1..15532</a>
%e A372292 21 is present because A371094(1) = A371094(3) = 21.
%e A372292 87381 is present because A371094(85) = A371094(213) = A371094(7281) = A371094(14563) = 87381.
%e A372292 185685 is present because A371094(469) = A371094(15473) = A371094(30947) = 185685.
%o A372292 (PARI)
%o A372292 A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372292 isA372292(n) = if(!(n%2),0,my(c=0); forstep(k=1,n,2,if(A371094(k)==n,c++)); (c>1));
%o A372292 (PARI)
%o A372292 search_up_to = 1398101;
%o A372292 A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372292 A372292list(up_to_n) = { my(v=vector((1+up_to_n)/2), x, lista=List([])); forstep(k=1,up_to_n,2,x=A371094(k); if(x <= up_to_n, v[(x+1)/2]++)); for(i=1,(1+up_to_n)/2,if(v[i]>1, listput(lista,i+i-1))); Vec(lista); };
%o A372292 v372292 = A372292list(search_up_to);
%o A372292 A372292(n) = v372292[n];
%Y A372292 Setwise difference A372290 \ A372291.
%Y A372292 Cf. A144864 (subsequence after its initial 1), A371094, A371100.
%K A372292 nonn
%O A372292 1,1
%A A372292 _Antti Karttunen_, Apr 26 2024