

A114137


Difference between first odd semiprime > 2^n and 2^n.


0



8, 7, 5, 1, 5, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 5, 9, 1, 5, 1, 1, 5, 7, 1, 3, 3, 3, 3, 1, 9, 25, 1, 1, 11, 7, 3, 7, 15, 19, 3, 1, 5, 3, 1, 31, 3, 7, 21, 3, 9, 7, 11, 3, 11, 3, 29, 9, 29, 25, 9, 45, 1, 3, 9, 1
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OFFSET

0,1


COMMENTS

A098147 is difference between first odd semiprime > 10^n and 10^n. In this powers of 2 sequence, does 1 occur infinitely often? Does every odd number occur?


LINKS

Table of n, a(n) for n=0..64.


FORMULA

a(n) = minimum integer k such that 2^n + k is an element of A046315. a(n) = minimum integer k such that A000079(n) + k is an element of A046315.


EXAMPLE

a(0) = 8 (the only even value here) because 2^0 + 8 = 9 = 3^2 is an odd semiprime.
a(1) = 7 because 2^1 + 7 = 9 = 3^2 is an odd semiprime.
a(2) = 5 because 2^2 + 5 = 9 = 3^2 is an odd semiprime.
a(3) = 1 because 2^3 + 1 = 9 = 3^2 is an odd semiprime.
a(4) = 5 because 2^4 + 5 = 21 = 3 * 7 is an odd semiprime.
a(5) = 1 because 2^5 + 1 = 33 = 3 * 11 is an odd semiprime.
a(6) = 1 because 2^6 + 1 = 65 = 5 * 13 is an odd semiprime.
a(10) = 3 because 2^10 + 3 = 1027 = 13 * 79 is an odd semiprime.
a(30) = 25 because 2^30 + 25 = 1073741849 = 29 * 37025581 is an odd semiprime.


MATHEMATICA

a[n_] := Block[{z}, If[n == 0, z = 3, z = 2^n + 1]; While[ PrimeOmega[z] != 2, z += 2]; z  2^n]; a /@ Range[0, 64] (* Giovanni Resta, Jun 14 2016 *)


CROSSREFS

Cf. A001358, A098147.
Sequence in context: A019903 A167222 A076417 * A185346 A200017 A316728
Adjacent sequences: A114134 A114135 A114136 * A114138 A114139 A114140


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 03 2006


EXTENSIONS

a(46) corrected by Giovanni Resta, Jun 14 2016


STATUS

approved



