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A088363 Local minima of A053707 (first differences of A025475, powers of a prime but not prime). 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A163485 A276011 A126038 * A300839 A143783 A179175
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Sep 27 2003
STATUS
approved

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Last modified April 16 22:26 EDT 2024. Contains 371755 sequences. (Running on oeis4.)