A228157 -id:A228157 - cp's OEIS frontend

A379208 Numbers k such that prime(k) and prime(k) + 9 are anagrams.

9, 19, 24, 26, 39, 48, 73, 77, 79, 91, 99, 110, 126, 143, 163, 188, 197, 200, 209, 212, 219, 224, 237, 241, 247, 252, 262, 269, 278, 279, 281, 285, 290, 291, 316, 336, 355, 360, 365, 391, 403, 405, 408, 431, 434, 439, 442, 448, 464, 468, 477, 486, 507, 517, 524, 531, 539, 544, 549, 550, 551, 575, 589, 602, 615

Offset: 1

Vincenzo Librandi, Dec 18 2024

			9 is a term of the sequence because prime(9) = 23 and 23 + 9 = 32 are anagrams.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A140353, A228157.

[n: n in [0..2000] | Sort(Intseq(NthPrime(n))) eq Sort(Intseq(NthPrime(n) + 9))];

filter:= proc(k) local p;
  p:= ithprime(k);
  sort(convert(p,base,10)) = sort(convert(p+9,base,10))
end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 18 2025

Select[Range[3000],Sort[IntegerDigits[Prime[#]]]==Sort[IntegerDigits[Prime[#]+9]]&]

is(n) = my(p = prime(n)); vecsort(digits(p)) == vecsort(digits(p+9)) \\ David A. Corneth, Dec 18 2024

Name corrected by David A. Corneth, Dec 18 2024

A363820 Moving the rightmost digit of a number to place it furthest to the left adds 9 to the number.

Original entry on oeis.org

12, 23, 34, 45, 56, 67, 78, 89, 101, 212, 323, 434, 545, 656, 767, 878, 989, 1101, 2212, 3323, 4434, 5545, 6656, 7767, 8878, 9989, 11101, 22212, 33323, 44434, 55545, 66656, 77767, 88878, 99989, 111101, 222212, 333323, 444434, 555545, 666656, 777767, 888878, 999989

Offset: 1

Eric Angelini, Oct 18 2023

All terms k are repdigit numbers minus 10. The sequence starts with 22 - 10 = 12. - Andrew Howroyd, Oct 22 2023

			a(1) = 12 plus 9 = 21; the rightmost 2 is now in front and 1 at the end;
a(2) = 23 plus 9 = 32; the rightmost 3 is now in front and 2 at the end;
a(3) = 34 plus 9 = 43; the rightmost 4 is now in front and 3 at the end;
a(4) = 45 plus 9 = 54; the rightmost 5 is now in front and 4 at the end;
...
a(9) = 101 plus 9 = 110; the rightmost 1 is now in front and 0 at the end; etc.

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Cf. A010785 (repdigit numbers), A228157, A363823.

Select[Range[10^6],FromDigits[RotateRight[IntegerDigits[#]]]-#==9 &] (* Stefano Spezia, Oct 18 2023 *)

a(n) = if(n > 0, (n%9 + 1)*(10^(n\9 + 2)-1)/9 - 10) \\ Andrew Howroyd, Oct 22 2023

def ok(n): s = str(n); return int(s[-1]+s[:-1]) - n == 9
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Oct 18 2023

A382118 Prime indices k such that prime(k) and prime(k) + 9 are anagrams.

Original entry on oeis.org

19, 73, 79, 163, 197, 241, 269, 281, 431, 439, 619, 647, 691, 739, 751, 761, 823, 877, 953, 1019, 1051, 1109, 1223, 1259, 1291, 1307, 1423, 1471, 1723, 1741, 1747, 1847, 1949, 1979, 2213, 2371, 2473, 2503, 2647, 2789, 2803, 2819, 2879, 2903, 2909, 3019, 3163, 3361

Offset: 1

Vincenzo Librandi, Apr 15 2025

Primes in A379208.

			The prime 19 is a term of the sequence because prime(19)= 67 and 67 + 9 = 76 are anagrams.

Vincenzo Librandi, Table of n, a(n) for n = 1..19861

Cf. A140353, A228157, A379208.

[n: n in [0..10000] | IsPrime(n) and Sort(Intseq(NthPrime(n))) eq Sort(Intseq(NthPrime(n) + 9))];

Select[Prime[Range[500]],Sort[IntegerDigits[Prime[#]]]==Sort[IntegerDigits[Prime[#]+9]]&]

A266912 Numbers n which are anagrams of n+18.

Original entry on oeis.org

13, 24, 35, 46, 57, 68, 79, 102, 113, 124, 135, 146, 157, 168, 179, 202, 213, 224, 235, 246, 257, 268, 279, 302, 313, 324, 335, 346, 357, 368, 379, 402, 413, 424, 435, 446, 457, 468, 479, 502, 513, 524, 535, 546, 557, 568, 579, 602, 613, 624, 635, 646, 657

Offset: 1

Vincenzo Librandi, Jan 06 2016

n is an anagram of n+k when k is a multiple of 9.

			24 is a term of the sequence because 24 and 24+18 = 42 are anagrams.

Cf. A228157.

[n: n in [0..700] | Sort(Intseq(n)) eq Sort(Intseq(n+18))]; // Bruno Berselli, Jan 08 2016

Select[Range[0, 600], Sort[IntegerDigits[#]] == Sort[IntegerDigits[# + 18]] &] (* or *) Reap[Do[If[Sort@IntegerDigits[n] == Sort@IntegerDigits[n + 18], Sow[n]], {n, 600}]][[-1, 1]]

isok(n) = vecsort(digits(n)) == vecsort(digits(n+18)); \\ Michel Marcus, Jan 08 2016

From Chai Wah Wu, Dec 23 2016: (Start)
a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9.
G.f.: x*(-2*x^8 + 23*x^7 + 11*x^6 + 11*x^5 + 11*x^4 + 11*x^3 + 11*x^2 + 11*x + 13)/(x^9 - x^8 - x + 1).
First difference is 8-periodic: 11,11,11,11,11,11,23,11,... (End)

cp's OEIS Frontend

A379208 Numbers k such that prime(k) and prime(k) + 9 are anagrams.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Extensions

A363820 Moving the rightmost digit of a number to place it furthest to the left adds 9 to the number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A382118 Prime indices k such that prime(k) and prime(k) + 9 are anagrams.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A266912 Numbers n which are anagrams of n+18.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Mathematica

PARI

Formula