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A088364 a(n) = index of the n-th local minimum of A053707. 2

%I #9 Aug 24 2023 07:30:57

%S 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 73,75,78,80,82,86,90,94,96,98,102,105,108,112,115,119,124,128,132,

%U 134,136,139,141,144,146,148,150,152,156,158,160,165,168,171,173,176,180,182

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

%H Robert Israel, <a href="/A088364/b088364.txt">Table of n, a(n) for n = 1..10000</a>

%F A053707(a(n)) = A088363(n).

%e 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 N:= 10^6: # to use values of A025475 up to N

%p P:= select(isprime, [2,seq(i,i=3..isqrt(N),2)]):

%p B:= sort([1,seq(seq(p^i,i=2..ilog[p](N)),p=P)]):

%p DB:= B[2..-1]-B[1..-2]:

%p T:= select(t -> DB[t] <= DB[t-1] and DB[t] <= DB[t+1], [$2..nops(DB)-1]):

%p [1,op(T)]; # _Robert Israel_, Aug 21 2023

%o (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 Cf. A025475, A053707, A088363.

%K nonn

%O 1,2

%A _Klaus Brockhaus_, Sep 27 2003

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Last modified April 17 10:33 EDT 2024. Contains 371763 sequences. (Running on oeis4.)