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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)