cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

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

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Crossrefs

Cf. A096508-A096519.

A096843 Primes of form repdigit - 1. Primes whose sum of divisors is a decimal repdigit.

Original entry on oeis.org

2, 3, 5, 7, 43, 443, 887, 2221, 8887, 444443, 888887, 444444443, 888888887, 444444444443, 888888888887, 222222222222222221, 444444444444444444444444444443, 44444444444444444444444444444443
Offset: 1

Views

Author

Labos Elemer, Jul 15 2004

Keywords

Comments

Union numbers 2, 5 and sequences A093171, A093163 and A091189.
Corresponding values of sigma(a(n)) are in A028987. - Jaroslav Krizek, Mar 19 2013

Examples

			n=43: sigma(43)=44;

Links

Crossrefs

Cf. A096503-A096508, A096841-A096846, A000203.

Extensions

Missing a(1)=2 and a(3)=5 added by Jaroslav Krizek, Mar 19 2013

A096510 a(n) is the smallest number x such that the number of prime powers (including primes, excluding 1), in the neighborhood of x with radius ceiling(log(x)), equals n.

Original entry on oeis.org

1, 54, 2, 12, 3, 8, 4792, 75991, 284736, 6561003, 51448375, 964669618, 18320500423
Offset: 0

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Comments

With increasing n the radius of log(n) slowly increases, while frequency of prime-powers decreases.
No more terms < 369*10^8. - David Wasserman, Nov 16 2007

Examples

			a[8]=284736: because in [284723,284749] around a(8),
8 prime(powers) occur first,with radius=r=13;
a[0]=1;a[1]=54 means that in [50,58] only 53 is prime,r=4.

Crossrefs

Cf. A096508-A096512.
Cf. A096509-A096523.

Extensions

4 more terms from David Wasserman, Nov 16 2007

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

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Crossrefs

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

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Examples

			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.

Crossrefs

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

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Examples

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

Crossrefs

Cf. A096508-A096519.

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

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Examples

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

Crossrefs

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

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Examples

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

Crossrefs

Cf. A096508-A096519.

A096842 Sigma applied to A096841 produces these repdigits: a[n]=A000203[A096841(n)].

Original entry on oeis.org

1, 3, 4, 7, 6, 8, 44, 222, 444, 888, 444, 888, 888, 2222, 6666, 8888, 8888, 222222, 88888, 222222, 444444, 444444, 888888, 444444, 444444, 666666, 888888, 888888, 888888, 888888, 888888, 444444, 444444, 888888, 888888, 888888, 888888, 888888
Offset: 1

Views

Author

Labos Elemer, Jul 15 2004

Keywords

Examples

			n=43:sigma[43]=44;

Crossrefs

Cf. A096503-A096508, A096841-A096846, A000203.

Programs

  • Mathematica
    rd[x_] := Length[Union[IntegerDigits[x]]] Do[s = rd[DivisorSigma[1, n]]; s1 = DivisorSigma[1, n]; If[Equal[s, 1], Print[{n, s1}]; ta[[u]] = n; u = u + 1], {n, 1, 1000000}];ta;DivisorSigma[1, ta]

A294396 Numbers k such that 12*10^k + 1 is prime.

Original entry on oeis.org

0, 2, 38, 80, 9230, 25598, 39500
Offset: 1

Views

Author

Patrick A. Thomas, Feb 12 2018

Keywords

Comments

k must be even since 12*10^k + 1 is divisible by 11 if k is odd. - Robert G. Wilson v, Feb 12 2018
a(7) > 27440. - Robert G. Wilson v, Feb 17 2018
a(8) > 10^5. - Jeppe Stig Nielsen, Jan 31 2023

Examples

			13 and 1201 are prime, so 0 and 2 are the initial values.

Crossrefs

Cf. A001562, A096507, A056797, A056807, A056806, A102940, A056805, A056804, A096508, A102975, A289051, A099017, A295325, A273002, A102945, A282456, A267420.
Cf. A062339 (primes with digit sum 4).

Programs

  • Mathematica
    ParallelMap[ If[ PrimeQ[12*10^# +1], #, Nothing] &, 2 + 6Range@ 4500] (* Robert G. Wilson v, Feb 13 2018 *)
  • PARI
    isok(k) = isprime(12*10^k + 1); \\ Altug Alkan, Mar 04 2018

Extensions

a(5) from Robert G. Wilson v, Feb 12 2018
a(6) from Robert G. Wilson v, Feb 13 2018
a(7) from Jeppe Stig Nielsen, Jan 28 2023
Previous Showing 11-20 of 20 results.

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