A088364 - OEIS

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

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OFFSET

1,2

LINKS

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

FORMULA

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

EXAMPLE

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).

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

PROG

(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))}

CROSSREFS

Cf. A025475, A053707, A088363.

Sequence in context: A338763 A159908 A236761 * A022853 A198264 A186516

Adjacent sequences: A088361 A088362 A088363 * A088365 A088366 A088367

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Sep 27 2003

STATUS

approved