A339506 - OEIS

A339506

Numbers surviving a repeated sieving process for pseudo-lucky numbers (A249876).

1, 3, 5, 7, 13, 17, 31, 35, 41, 43, 47, 63, 101, 105, 107, 131, 175, 177, 185, 211, 235, 237, 267, 301, 305, 315, 323, 397, 407, 451, 571, 631, 633, 683, 757, 841, 877, 947, 987, 1043, 1221, 1251, 1431, 1501, 1655, 1781, 1961, 1981, 2023, 2067, 2157, 2197, 2253, 2367, 2457, 2505, 2615 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Start with the positive integers as the 1st starting sequence. The 1st full sieving process for the pseudo-lucky numbers begins with the 2nd term in the 1st starting sequence and generates A249876 (the 2nd starting sequence). The n-th full sieving process begins with the (n+1)-th term in the n-th starting sequence and generates the (n+1)-th starting sequence. The numbers that are left form the final sequence.` `Let b(m) be the number of elements of this sequence <= m. Let c(m) = round(square(sm/log(sm))), where s = 11.` `--------------------------------` `m \| b(m) \| c(m) \| b(m)-c(m)` `--------------------------------` `10^2 \| 12 \| 13 \| -1` `10^3 \| 39 \| 34 \| +5` `10^4 \| 103 \| 97 \| +6` `510^4 \| 210 \| 204 \| +6` `610^4 \| 228 \| 222 \| +6` `710^4 \| 236 \| 238 \| -2` `810^4 \| 256 \| 254 \| +2` `9*10^4 \| 270 \| 268 \| +3` `10^5 \| 282 \| 281 \| +1` `--------------------------------` `Is c(m) an approximation to b(m)?`
	LINKS	`Table of n, a(n) for n=1..57.`
	EXAMPLE	`The 1st full sieving process:` `1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ...` `1 X 3 X 5 X 7 X 9 X 11 X 13 X 15 X 17 X 19 X 21 X 23 X 25 ...` `1 3 5 7 X 11 13 15 17 X 21 23 25 ...` `1 3 5 7 11 13 X 17 21 23 25 ...` `Continuing the above procedure generates the 2nd starting sequence (the pseudo-lucky numbers) to begin the 2nd full sieving process:` `1 3 5 7 11 13 17 21 23 25 31 35 41 43 45 47 55 57 63 65 73 75 83 87 95 ...` `1 3 5 7 X 13 17 21 23 X 31 35 41 43 X 47 55 57 63 X 73 75 83 87 X ...` `1 3 5 7 13 17 X 23 31 35 41 43 47 X 57 63 73 75 83 87 ...` `1 3 5 7 13 17 23 31 35 41 43 47 X 63 73 75 83 87 ...` `1 3 5 7 13 17 23 31 35 41 43 47 63 73 75 83 X ...` `Continuing the above procedure generates the 3rd starting sequence to begin the 3rd full sieving process:` `1 3 5 7 13 17 23 31 35 41 43 47 63 73 75 83 101 105 107 123 127 131 151 ...` `1 3 5 7 13 17 X 31 35 41 43 47 63 X 75 83 101 105 107 123 X 131 151 ...` `1 3 5 7 13 17 31 35 41 43 47 63 X 83 101 105 107 123 131 151 ...` `1 3 5 7 13 17 31 35 41 43 47 63 83 101 105 107 X 131 151 ...` `Continuing the above procedure generates the 4th starting sequence to begin the 4th full sieving process:` `1 3 5 7 13 17 31 35 41 43 47 63 83 101 105 107 131 151 153 175 177 185 ...` `1 3 5 7 13 17 31 35 41 43 47 63 X 101 105 107 131 151 153 175 177 185 ...` `1 3 5 7 13 17 31 35 41 43 47 63 101 105 107 131 X 153 175 177 185 ...` `Continuing the above procedure generates the 5th starting sequence to begin the 5th full sieving process:` `1 3 5 7 13 17 31 35 41 43 47 63 101 105 107 131 153 175 177 185 211 235 ...` `1 3 5 7 13 17 31 35 41 43 47 63 101 105 107 131 X 175 177 185 211 235 ...` `...` `Continue forever and the numbers not crossed off give the sequence.`
	CROSSREFS	`Cf. A000959, A249876.` `Sequence in context: A038929 A242755 A070806 * A178490 A182981 A234388` `Adjacent sequences: A339503 A339504 A339505 * A339507 A339508 A339509`
	KEYWORD	`nonn`
	AUTHOR	`Lechoslaw Ratajczak, Dec 07 2020`
	STATUS	`approved`