A074997 -id:A074997 - cp's OEIS frontend

A086540 Numbers n such that n and n+1 both are members of A074997; i.e., on the one hand n-1 and n+1 have the same prime signature, on the other hand n and n+2 have the same prime signature.

18, 55, 248, 340, 348, 722, 850, 949, 1061, 1148, 1204, 1205, 1241, 1277, 1314, 1315, 1667, 1672, 2148, 2716, 2948, 2949, 3258, 3581, 3650, 3651, 4044, 4265, 4627, 4842, 5092, 5093, 5451, 5741, 5765, 6244, 6355, 6356, 6565, 6640, 6851, 6963, 7362, 7404

Offset: 1

Amarnath Murthy, Aug 22 2003

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A074997.

isok1(n) = vecsort(factor(n-1)[,2]) == vecsort(factor(n+1)[,2]);
isok(n) = isok1(n) && isok1(n+1); \\ Michel Marcus, Jul 28 2015

More terms from David Wasserman, Mar 21 2005

A074996 Floor of concatenation of n, n+1, n+2, n+3, n+4, n+5 divided by 6.

Original entry on oeis.org

2057, 20576, 39094, 57613, 76131, 946485, 11315168, 131516852, 1485018535, 15168520219, 16852021902, 18535523586, 20219025269, 21902526953, 23586028636, 25269530320, 26953032003, 28636533687, 30320035370

Offset: 0

Amarnath Murthy, Aug 31 2002

Cf. A074991, A074992, A074993, A074994, A074995, A074997, A073086, A074999.

Table[Floor[FromDigits[Flatten[IntegerDigits[Range[n,n+5]]]]/6],{n,0,18}] (* Jayanta Basu, May 22 2013 *)

Edited by Dean Hickerson, Nov 03 2002

A074993 a(n) = floor((concatenation of n, n+1)/2).

Original entry on oeis.org

0, 6, 11, 17, 22, 28, 33, 39, 44, 455, 505, 556, 606, 657, 707, 758, 808, 859, 909, 960, 1010, 1061, 1111, 1162, 1212, 1263, 1313, 1364, 1414, 1465, 1515, 1566, 1616, 1667, 1717, 1768, 1818, 1869, 1919, 1970, 2020, 2071, 2121, 2172, 2222, 2273, 2323, 2374

Offset: 0

Amarnath Murthy, Aug 31 2002

The first differences follow a pattern. Odd-indexed terms and even-indexed terms form separate A.P.s with the same common difference for all n except n = 10^k -1. The corresponding common differences are the repunits = (10^(d+1)-1)/9 where d = the number of digits in n.

Cf. A001704, A074991, A074992, A074994, A074995, A074996, A074997, A073086, A074999, A127421.

cc[n_]:=Floor[FromDigits[Join[IntegerDigits[n],IntegerDigits[n+1]]]/2]; Array[cc,40,0] (* Harvey P. Dale, Nov 11 2011 *)

A074994 Floor of concatenation of n, n+1, n+2, n+3 divided by 4.

Original entry on oeis.org

30, 308, 586, 864, 1141, 1419, 1697, 19727, 222752, 2275278, 2527803, 2780328, 3032853, 3285379, 3537904, 3790429, 4042954, 4295480, 4548005, 4800530, 5053055, 5305581, 5558106, 5810631, 6063156, 6315682, 6568207, 6820732

Offset: 0

Amarnath Murthy, Aug 31 2002

			a(7) = floor(78910/4) = 19727.

Cf. A074991, A074992, A074993, A074995, A074996, A074997, A073086, A074999.

Edited by Dean Hickerson, Nov 03 2002

A074995 Floor of concatenation of n, n+1, n+2, n+3, n+4 divided by 5.

Original entry on oeis.org

246, 2469, 4691, 6913, 9135, 11357, 135782, 1578202, 17820222, 182022242, 202224262, 222426283, 242628303, 262830323, 283032343, 303234363, 323436384, 343638404, 363840424, 384042444, 404244464, 424446485, 444648505, 464850525

Offset: 0

Amarnath Murthy, Aug 31 2002

Cf. A074991, A074992, A074993, A074994, A074996, A074997, A073086, A074999.

Edited by Dean Hickerson, Nov 03 2002

A280383 Numbers n such that n-1 has the same count of prime factors as n+1 when including multiplicity and also when not.

Original entry on oeis.org

4, 6, 12, 18, 19, 30, 34, 42, 51, 55, 56, 60, 72, 86, 92, 94, 102, 108, 138, 142, 144, 150, 160, 180, 184, 186, 192, 198, 202, 204, 214, 216, 218, 220, 228, 236, 240, 243, 248, 249, 266, 270, 282, 300, 302, 304, 307, 312, 320, 322, 328, 340, 341, 348, 349, 392, 394, 412, 414, 416, 420, 424, 432, 446, 452, 462, 470, 472, 476, 491, 516, 518, 522, 534, 536, 544, 552, 570, 580, 582, 590, 600, 604, 618, 634, 638, 642, 660, 664, 668, 670, 680, 686, 688, 696, 698, 701, 722

Offset: 1

Rick L. Shepherd, Jan 02 2017

nonn

First differs from its subsequence A074997 at a(97) = 701 because A074997(97) = 722.

			The number 19 is a term because 18 = 2*3^2 and 20 = 2^2*5 each have two distinct prime factors and each have three prime factors when counted with multiplicity.

Rick L. Shepherd, Table of n, a(n) for n = 1..10000

Cf. A001221, A001222, A074997, A088070, A280382.

Select[Range[800],PrimeNu[#]==PrimeNu[#+2]&&PrimeOmega[#]==PrimeOmega[#+2]&]+1 (* Harvey P. Dale, Jul 12 2023 *)

IsInA280383(n) = n > 1 && bigomega(n-1) == bigomega(n+1) && omega(n-1) == omega(n+1)

Sequence is A088070 INTERSECT A280382.

A074998 Composite numbers which are sandwiched between two numbers having the same unordered canonical form.

Original entry on oeis.org

4, 6, 12, 18, 30, 34, 42, 51, 55, 56, 60, 72, 86, 92, 94, 102, 108, 138, 142, 144, 150, 160, 180, 184, 186, 192, 198, 202, 204, 214, 216, 218, 220, 228, 236, 240, 243, 248, 249, 266, 270, 282, 300, 302, 304, 312, 320, 322, 328, 340, 341, 348, 392, 394, 412

Offset: 1

Amarnath Murthy, Aug 21 2002

nonn

The average of twin primes is a member.

			34 is sandwiched between 33 and 35 which are of the form p*q where p and q are primes.

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

Cf. A074997, A061715, A074460.

k := 0: for j from 2 to 5000 do if not isprime(j) then a := ifactors(j-1): b := ifactors(j+1): if sort([seq(a[2][i][2],i= 1..nops(a[2]))])= sort([seq(b[2][i][2],i= 1..nops(b[2]))]) then k := k+1: c[k] := j: fi: fi: od: seq(c[i],i= 1..k);

More terms from Sascha Kurz, Aug 22 2002

Offset corrected by Amiram Eldar, Jan 02 2020

cp's OEIS Frontend

A086540 Numbers n such that n and n+1 both are members of A074997; i.e., on the one hand n-1 and n+1 have the same prime signature, on the other hand n and n+2 have the same prime signature.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Extensions

A074996 Floor of concatenation of n, n+1, n+2, n+3, n+4, n+5 divided by 6.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Extensions

A074993 a(n) = floor((concatenation of n, n+1)/2).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A074994 Floor of concatenation of n, n+1, n+2, n+3 divided by 4.

Views

Author

Keywords

Examples

Crossrefs

Extensions

A074995 Floor of concatenation of n, n+1, n+2, n+3, n+4 divided by 5.

Views

Author

Keywords

Crossrefs

Extensions

A280383 Numbers n such that n-1 has the same count of prime factors as n+1 when including multiplicity and also when not.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A074998 Composite numbers which are sandwiched between two numbers having the same unordered canonical form.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Extensions