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

1, 3, 6, 9, 13, 16, 19, 21, 26, 28, 30, 33, 37, 39, 43, 48, 50, 53, 56, 61, 63, 66, 68, 70, 73, 75, 78, 80, 82, 86, 90, 94, 96, 98, 102, 105, 108, 112, 115, 119, 124, 128, 132, 134, 136, 139, 141, 144, 146, 148, 150, 152, 156, 158, 160, 165, 168, 171, 173, 176, 180, 182

Offset: 1

Author

Klaus Brockhaus, Sep 27 2003

Keywords

• nonn

Examples

			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).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025475, A053707, A088363.

Programs

Maple

N:= 10^6: # to use values of A025475 up to N
P:= select(isprime, [2,seq(i,i=3..isqrt(N),2)]):
B:= sort([1,seq(seq(p^i,i=2..ilog[p](N)),p=P)]):
DB:= B[2..-1]-B[1..-2]:
T:= select(t -> DB[t] <= DB[t-1] and DB[t] <= DB[t+1], [$2..nops(DB)-1]):
[1,op(T)]; # Robert Israel, Aug 21 2023

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))}

Formula

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