A088363 - OEIS

A088363

Local minima of A053707 (first differences of A025475, powers of a prime but not prime).

3, 1, 2, 15, 3, 13, 18, 17, 63, 38, 168, 10, 316, 240, 128, 30, 271, 408, 286, 255, 354, 362, 600, 260, 672, 138, 7, 768, 792, 876, 960, 513, 248, 1080, 546, 2328, 1248, 4008, 1392, 751, 2188, 250, 94, 1728, 3528, 3470, 1848, 2460, 3912, 4008, 3063, 2088, 1554

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OFFSET

1,1

COMMENTS

A053707(k) for k = 1 is a term iff A053707(k) <= A053707(k+1); A053707(k) for k > 1 is a term iff A053707(k-1) > A053707(k) and A053707(k) <= A053707(k+1).

A088364 gives the corresponding indices. Local maxima of A053707 are in A088365.

LINKS

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

EXAMPLE

The first four terms of A053707 are 3,4,1,7, hence A053707(1) = 3 is the first and A053707(3) = 1 is the second local minimum of A053707.

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]):

DB[[1, op(T)]]; # Robert Israel, Aug 21 2023

PROG

(PARI) {m=1; k=0; for(n=2, 320000, if(matsize(factor(n))[1]==1&&factor(n)[1, 2]>1, d=n-m; if((k<2||b>c)&&(!k<1&&d>=c), print1(c, ", ")); k++; m=n; b=c; c=d))}

CROSSREFS

Cf. A025475, A053707, A088364, A088365.

Sequence in context: A163485 A276011 A126038 * A300839 A143783 A179175

Adjacent sequences: A088360 A088361 A088362 * A088364 A088365 A088366

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Sep 27 2003

STATUS

approved