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A114137
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Difference between first odd semiprime > 2^n and 2^n.
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0
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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, 9, 21, 3, 9, 7, 11, 3, 11, 3, 29, 9, 29, 25, 9, 45, 1, 3, 9, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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?
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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.
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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.
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CROSSREFS
| Cf. A001358, A098147.
Sequence in context: A019903 A167222 A076417 * A200017 A072003 A160668
Adjacent sequences: A114134 A114135 A114136 * A114138 A114139 A114140
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 03 2006
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