

A053707


First differences of A025475, powers of a prime but not prime.


12



3, 4, 1, 7, 9, 2, 5, 17, 15, 17, 40, 4, 3, 41, 74, 13, 33, 54, 18, 151, 17, 96, 104, 112, 120, 63, 307, 38, 312, 168, 199, 139, 10, 12, 192, 408, 316, 356, 240, 375, 393, 424, 128, 288, 912, 320, 298, 30, 1032, 271, 1217, 792, 408, 840, 432, 286, 602, 1872, 984, 504
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OFFSET

1,1


COMMENTS

In the graph of this sequence, the lowest curve corresponds to differences of squares of twin primes; the nextlowest curve is for squares of adjacent primes differing by 4, etc.  T. D. Noe, Aug 03 2007


LINKS

T. D. Noe, Table of n, a(n) for n=1..10000


FORMULA

a(n) = A025475(n+1)  A025475(n).


EXAMPLE

2^0 = 1 is the first number that meets the definition of A025475, the next one is 2^2 = 4, hence a(1) = 4  1 = 3.
a(3) = A025475(4)  A025475(3) = 9  8 = 1; a(11) = A025475(12)  A025475(11) = 121  81 = 40.


MATHEMATICA

Differences@ Join[{1}, Select[Range@ 16200, And[! PrimeQ@ #, PrimePowerQ@ #] &]] (* Michael De Vlieger, Jul 04 2016 *)


PROG

(PARI) {k=1; for(n=2, 16300, if(matsize(factor(n))[1]==1&&factor(n)[1, 2]>1, d=nk; print1(d, ", "); k=n))} \\ Klaus Brockhaus, Sep 25 2003


CROSSREFS

Cf. A025475.
Sequence in context: A076446 A053289 A076412 * A075052 A111516 A210636
Adjacent sequences: A053704 A053705 A053706 * A053708 A053709 A053710


KEYWORD

nonn


AUTHOR

Labos Elemer, Feb 14 2000


EXTENSIONS

Edited by Klaus Brockhaus, Sep 25 2003


STATUS

approved



