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

Offset: 1

Author

Klaus Brockhaus, Sep 27 2003

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A025475, A053707, A088364, A088365.

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

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))}