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A088364 a(n) = index of the n-th local minimum of A053707.

%I A088364 #13 Aug 25 2024 02:44:45
%S A088364 1,3,6,9,13,16,19,21,26,28,30,33,37,39,43,48,50,53,56,61,63,66,68,70,
%T A088364 73,75,78,80,82,86,90,94,96,98,102,105,108,112,115,119,124,128,132,
%U A088364 134,136,139,141,144,146,148,150,152,156,158,160,165,168,171,173,176,180,182
%N A088364 a(n) = index of the n-th local minimum of A053707.
%H A088364 Robert Israel, <a href="/A088364/b088364.txt">Table of n, a(n) for n = 1..10000</a>
%F A088364 A053707(a(n)) = A088363(n).
%e A088364 The eighth local minimum of A053707 is 17 and occurs at index 21, hence a(8) = 21; A053707(a(8)) = A053707(21) = 17 = A088363(8).
%p A088364 N:= 10^6: # to use values of A025475 up to N
%p A088364 P:= select(isprime, [2,seq(i,i=3..isqrt(N),2)]):
%p A088364 B:= sort([1,seq(seq(p^i,i=2..ilog[p](N)),p=P)]):
%p A088364 DB:= B[2..-1]-B[1..-2]:
%p A088364 T:= select(t -> DB[t] <= DB[t-1] and DB[t] <= DB[t+1], [$2..nops(DB)-1]):
%p A088364 [1,op(T)]; # _Robert Israel_, Aug 21 2023
%o A088364 (PARI) {m=1; k=0; for(n=2,530000,if(matsize(factor(n))[1]==1&&factor(n)[1,2]>1,d=n-m; if((k<2||b>c)&&(!k<1&&d>=c),print1(k,",")); k++; m=n; b=c; c=d))}
%Y A088364 Cf. A025475, A053707, A088363.
%K A088364 nonn
%O A088364 1,2
%A A088364 _Klaus Brockhaus_, Sep 27 2003