A096509 -id:A096509 - cp's OEIS frontend

A096519 Solutions to A096509[x]=8, the number of prime-powers [including primes] in neighborhood of x with Ceiling[Log[x]] radius, equals 8.

284736, 595953, 855723, 855725, 855726, 855727, 1146785, 1146786, 1146787, 1616612, 1616618, 1616624, 1652884, 1654028, 1718708, 1749272, 1954358, 2176624, 2580658, 2580659, 2580660, 2580661, 2580662, 2831672, 2839942

Offset: 1

Labos Elemer, Jul 12 2004

nonn

Cf. A096508-A096518.

A096512 Numbers k such that A096509(k) = 1; i.e., the number of prime powers (including primes) in the neighborhood of k with radius ceiling(log(k)) is 1.

Original entry on oeis.org

54, 89, 90, 91, 95, 115, 119, 143, 145, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 296, 297, 298, 299, 301, 302, 303, 304, 320, 321, 322, 323, 325, 326, 327, 328, 329, 330, 390, 409, 410, 411, 471, 475, 476, 477, 478, 479, 531

Offset: 1

Labos Elemer, Jul 12 2004

nonn

Cf. A096508-A096519.

A096518 Solutions to A096509[x]=7; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 7.

Original entry on oeis.org

75991, 85841, 88801, 88805, 88807, 88808, 88809, 88810, 88811, 93491, 113155, 113159, 113161, 113165, 163984, 163985, 163986, 165708, 165709, 165710, 165711, 165712, 165713, 165714, 166854, 191454, 191460, 198828, 198829, 198830, 223836

Offset: 1

Labos Elemer, Jul 12 2004

nonn

Cf. A096508-A096519.

A096511 Numbers k such that A096509(k) = 0; i.e., the number of prime powers (including primes) in the neighborhood of k with radius ceiling(log(k)) is 0.

Original entry on oeis.org

1, 300, 324, 895, 896, 897, 898, 899, 1077, 1078, 1079, 1138, 1139, 1140, 1141, 1142, 1268, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1350, 1351, 1352, 1390, 1646, 1647, 1648, 1768, 1922, 1960, 1961, 1962, 1963, 1964, 2170, 2320, 2321

Offset: 1

Labos Elemer, Jul 12 2004

nonn

Cf. A096508-A096519.

A096513 Numbers k such that A096509(k) = 2; i.e., the number of prime powers (including primes) in the neighborhood of k with radius ceiling(log(k)) is 2.

Original entry on oeis.org

2, 36, 37, 38, 42, 48, 52, 53, 55, 73, 87, 88, 92, 93, 94, 96, 97, 113, 114, 116, 117, 118, 120, 121, 137, 138, 139, 140, 141, 142, 144, 146, 147, 148, 149, 150, 156, 158, 159, 160, 180, 181, 182, 183, 184, 186, 188, 189, 190, 200, 201, 202, 203, 205, 217, 221

Offset: 1

Labos Elemer, Jul 12 2004

nonn

			k=36 is a term: ceiling(log(36)) = ceiling(3.5835...) = 4, and in [36-4, 36+4] = [32, 40], 32 and 37 are the two corresponding powers of primes.

Cf. A096508-A096519.

A096514 Solutions to A096509[x]=3; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 3.

Original entry on oeis.org

12, 13, 15, 17, 18, 19, 20, 22, 24, 32, 34, 35, 39, 40, 41, 43, 44, 46, 47, 49, 50, 51, 56, 57, 58, 59, 60, 61, 65, 67, 70, 71, 72, 74, 75, 77, 79, 80, 81, 82, 83, 85, 86, 98, 99, 100, 101, 103, 107, 109, 110, 111, 112, 122, 131, 133, 134, 135, 136, 151, 152, 153, 154

Offset: 1

Labos Elemer, Jul 12 2004

nonn

			n=122: in [117,127] {121,125,127} are the 3 corresponding
powers of prime.

Cf. A096508-A096519.

A096515 Solutions to A096509[x]=4; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 4.

Original entry on oeis.org

3, 4, 5, 6, 7, 9, 11, 14, 16, 21, 23, 25, 26, 30, 31, 33, 45, 62, 63, 64, 66, 68, 69, 76, 78, 84, 102, 104, 105, 106, 108, 123, 124, 125, 127, 128, 129, 130, 132, 163, 167, 168, 169, 173, 175, 193, 194, 195, 196, 197, 227, 228, 229, 233, 235, 237, 238, 239, 245, 257

Offset: 1

Labos Elemer, Jul 12 2004

nonn

			n=63: in [58,68], {59,61,64,67} are the 4 corresponding prime powers.

A096516 Solutions to A096509[x]=5; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 5.

Original entry on oeis.org

8, 10, 27, 28, 29, 126, 1026, 1283, 1284, 1285, 1295, 1296, 1297, 1299, 1431, 1485, 1486, 1487, 1488, 1489, 1491, 1605, 1613, 1614, 1615, 1869, 1871, 1872, 1873, 1874, 1875, 1995, 2135, 2136, 2137, 2205, 2385, 2685, 2691, 2795, 2796, 2797, 3322, 3458

Offset: 1

Labos Elemer, Jul 12 2004

nonn

			n=126: in [121,131] {121,125,127,128,131} are the 5 corresponding
powers of prime.

Cf. A096508-A096519.

A096517 Solutions to A096509[x]=6; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 6.

Original entry on oeis.org

4792, 5648, 5650, 9429, 13687, 13688, 13689, 14553, 14631, 16063, 16064, 16065, 16066, 16067, 18051, 19423, 19424, 19425, 19426, 19427, 19431, 21021, 22280, 22281, 22282, 24102, 26690, 26691, 26692, 26720, 26721, 26722, 27740, 27741

Offset: 1

Labos Elemer, Jul 12 2004

nonn

			n=4792: in [4793,4801] {4783,4787,4789,4793,4799,4801} are the 6 corresponding
powers of prime.

Cf. A096508-A096519.

A096523 Solutions to A096520[x]>5, that is in neighborhood with c=2^x center and r=Ceiling[Log[2^x]] more than five[6,7,8,..?] primes occur.

Original entry on oeis.org

127, 505, 573, 619, 670, 714, 743, 844, 963

Offset: 1

Labos Elemer, Jul 12 2004

nonn

			For the first few terms, the numbers of primes in the corresponding neighborhood of 2^(a[j]) are 6, 6, 8, 6, 6, 6, 6, 7, 6.

Cf. A096509-A096521.

{ta=Table[0, {1000}], u=1}; Do[s=Count[Table[PrimeQ[2^n+i], {i, -Ceiling[Log[2^n]//N], Ceiling[Log[2^n]//N]}], True];If[Greater[s, 5], Print[{n, s}];ta[[u]]=n;u=u+1], {n, 1, 1000}];ta

cp's OEIS Frontend

A096519 Solutions to A096509[x]=8, the number of prime-powers [including primes] in neighborhood of x with Ceiling[Log[x]] radius, equals 8.

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A096512 Numbers k such that A096509(k) = 1; i.e., the number of prime powers (including primes) in the neighborhood of k with radius ceiling(log(k)) is 1.

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A096518 Solutions to A096509[x]=7; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 7.

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A096511 Numbers k such that A096509(k) = 0; i.e., the number of prime powers (including primes) in the neighborhood of k with radius ceiling(log(k)) is 0.

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A096513 Numbers k such that A096509(k) = 2; i.e., the number of prime powers (including primes) in the neighborhood of k with radius ceiling(log(k)) is 2.

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A096514 Solutions to A096509[x]=3; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 3.

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A096515 Solutions to A096509[x]=4; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 4.

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A096516 Solutions to A096509[x]=5; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 5.

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A096517 Solutions to A096509[x]=6; number of prime-powers [including primes] in the neighborhood of x with Ceiling[Log[x]] radius equals 6.

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A096523 Solutions to A096520[x]>5, that is in neighborhood with c=2^x center and r=Ceiling[Log[2^x]] more than five[6,7,8,..?] primes occur.

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Mathematica