A031158 -id:A031158 - cp's OEIS frontend

A031160 Twin lucky numbers (middle terms).

2, 8, 14, 32, 50, 68, 74, 128, 134, 170, 194, 236, 260, 284, 320, 392, 428, 476, 488, 518, 536, 578, 614, 620, 644, 728, 740, 884, 896, 926, 932, 980, 992, 1010, 1022, 1040, 1094, 1106, 1202, 1232, 1250, 1262, 1388, 1418, 1472, 1496, 1502

Offset: 1

Patrick De Geest

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000959, A031158, A031159, A031160.

Offset corrected by Amiram Eldar, Nov 15 2019

A031159 Twin lucky numbers (upper terms).

Original entry on oeis.org

3, 9, 15, 33, 51, 69, 75, 129, 135, 171, 195, 237, 261, 285, 321, 393, 429, 477, 489, 519, 537, 579, 615, 621, 645, 729, 741, 885, 897, 927, 933, 981, 993, 1011, 1023, 1041, 1095, 1107, 1203, 1233, 1251, 1263, 1389, 1419, 1473, 1497, 1503

Offset: 1

Patrick De Geest

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000959, A031158, A031159, A031160.

Offset corrected by Amiram Eldar, Nov 15 2019

A031884 Smaller of a pair of consecutive lucky numbers with a gap of 2n.

Original entry on oeis.org

1, 3, 15, 79, 141, 51, 787, 495, 171, 937, 903, 745, 2851, 1611, 1057, 3811, 5769, 4893, 8719, 10683, 9841, 24073, 9567, 28245, 25687, 3507, 26943, 35743, 44805, 51979, 64723, 23205, 50779, 51475, 264075, 155833, 238057, 178755, 143311, 400591, 223095, 181581, 466813

Offset: 1

Patrick De Geest

nonn

a(n) is the first occurrence of a difference of 2n between A000959(k+1) and A000959(k). - Robert G. Wilson v, May 12 2006
a(136) > 10^9. - Donovan Johnson, Dec 07 2011
Unknown terms a(166), a(176), a(178), a(182), and a(185) through a(209) are all greater than 10^10. - Kevin P. Thompson, Nov 24 2021

			a(4) = 79 since the lucky numbers A000959(20) = 79 and A000959(21) = 87 are the first consecutive pair with difference 2*4 = 8.

Kevin P. Thompson, Table of n, a(n) for n = 1..165 (terms 1..135 from Donovan Johnson)
Kevin P. Thompson, Table of n, a(n) for n = 1..210 with unknown terms

Cf. A000959, A031885, A031883, A031158, A031886, A031888, A031890, A031892, A031894, A031896, A031898, A031900, A031902.

lst = Range[1, 10^6, 2]; i = 2; While[ i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++ ]; f[n_] := Block[{k = 1}, While[t[[k + 1]] - t[[k]] != 2n, k++ ]; t[[k]]]; Array[f, 41] (* Robert G. Wilson v, May 12 2006 *)

More terms from Robert G. Wilson v, May 12 2006

A139783 Quadruple lucky numbers (lower terms). Numbers n such that n, n+2, n+6, n+8 are all Lucky numbers.

Original entry on oeis.org

1, 7, 67, 127, 613, 925, 1495, 1765, 2209, 2815, 3403, 5965, 6661, 8827, 9115, 15229, 16387, 18145, 19153, 21925, 23563, 24637, 27031, 27199, 28987, 31381, 32635, 34717, 35701, 36673, 40447, 43225, 43975, 47419, 50317, 51157, 56263, 64495

Offset: 1

Jonathan Vos Post, May 20 2008

Weisstein comments: "the frequency of twin primes and twin lucky numbers are similar." This is to lucky numbers A000959 and A031158 Twin lucky numbers (lower terms) as prime numbers A000040 and A001359 Lesser of twin primes are to A007530 Prime quadruples: numbers n such that n, n+2, n+6, n+8 are all prime.

			a(1) = 1 because 1, 1+2=3, 1+6=7 and 1+8=9 are all lucky numbers A000959.
a(2) = 7 because 7, 7+2=9, 7+6=13 and 7+8=15 are all lucky numbers A000959.
a(3) = 67 because {67, 69, 73, 75} are all lucky numbers.
a(4) = 127 because {127, 129, 133, 135} are all lucky numbers.
a(5) = 613 because {613, 615, 619, 621} are all lucky numbers.
a(6) = 925 because {925, 927, 931, 933} are all lucky numbers.
a(7) = 1495 because {1495, 1497, 1501, 1503} are all lucky numbers.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric W. Weisstein, Lucky Number.

Cf. A000040, A000959, A001359, A031158.

a(n) = {k such that k is in A000959 and k+2 is in A000959 and k+6 is in A000959 and k+8 is in A000959} = {k such that k is in A031158 and k+6 is in A031158}.

Inserted a(8)=1765 and extended, R. J. Mathar, Jul 18 2008

A289123 Numbers n such that (n-2,n) are twin primes, and (n,n+2) are twin lucky numbers.

Original entry on oeis.org

7, 13, 31, 73, 193, 283, 619, 643, 883, 1021, 1093, 1231, 2083, 2113, 2971, 3121, 3259, 4129, 4483, 4519, 5233, 6271, 6661, 6763, 7549, 7591, 8221, 9421, 10069, 10459, 10531, 11833, 12163, 13009, 13693, 13723, 13831, 17209, 17389, 20149, 20509, 21013, 21613

Offset: 1

Amiram Eldar, Jun 25 2017

nonn

Intersection of A006512 and A031158. Subsequence of A031157. The other case in which (n-2,n) are twin lucky numbers, and (n,n+2) are twin primes has only one solution, n = 3, since twin primes are of the form (6k-1, 6k+1) (except for 3 and 5) and 6k-1 is never lucky.

			7 is in the sequence since (5,7) are twin primes, and (7,9) are twin lucky numbers.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A006512, A000959, A031157, A031158.

L = Table[2*i + 1, {i, 0, 10^5}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]]; L[[Select[Range[1, Length[L] - 1], PrimeQ[L[[#]] - 2] && PrimeQ [L[[#]]] && L[[# + 1]] == L[[#]] + 2 &]]] (* after Jean-François Alcover at A000959 *)

A348771 a(n) = A031160(n)/2.

Original entry on oeis.org

1, 4, 7, 16, 25, 34, 37, 64, 67, 85, 97, 118, 130, 142, 160, 196, 214, 238, 244, 259, 268, 289, 307, 310, 322, 364, 370, 442, 448, 463, 466, 490, 496, 505, 511, 520, 547, 553, 601, 616, 625, 631, 694, 709, 736, 748, 751, 772, 793, 799, 820, 883, 886, 916, 961

Offset: 1

N. J. A. Sloane, Nov 06 2021

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000959, A031158, A031159, A031160.

More terms from Amiram Eldar, Mar 09 2022

A055725 Number of isolated lucky numbers <= 10^n.

Original entry on oeis.org

0, 0, 9, 87, 762, 6448, 56580, 498141, 4447890

Offset: 0

Robert G. Wilson v, Jun 09 2000

An isolated lucky number is a lucky number which is not a member of a lucky twin. The set of such numbers is A000959 setminus (A031158 union A031159). - Sean A. Irvine, Apr 04 2022

Cf. A000959, A031158, A031159.

a(7) and title clarified by Sean A. Irvine, Apr 04 2022

a(8) from Pontus von Brömssen, Apr 04 2022

cp's OEIS Frontend

A031160 Twin lucky numbers (middle terms).

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A031159 Twin lucky numbers (upper terms).

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A031884 Smaller of a pair of consecutive lucky numbers with a gap of 2n.

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A139783 Quadruple lucky numbers (lower terms). Numbers n such that n, n+2, n+6, n+8 are all Lucky numbers.

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A289123 Numbers n such that (n-2,n) are twin primes, and (n,n+2) are twin lucky numbers.

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A348771 a(n) = A031160(n)/2.

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A055725 Number of isolated lucky numbers <= 10^n.

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