A056964 -id:A056964 - cp's OEIS frontend

A366080 Numbers that give a perfect power when added to their reverse.

2, 4, 8, 29, 38, 47, 56, 65, 74, 83, 92, 110, 122, 143, 164, 198, 221, 242, 263, 297, 320, 341, 362, 396, 440, 461, 495, 560, 594, 693, 792, 891, 990, 1030, 1120, 1210, 1300, 10100, 10148, 10340, 10395, 10403, 10683, 10908, 10980, 11138, 11330, 11385, 11673

Offset: 1

Tanmaya Mohanty, Oct 24 2023

			8 is a term because 8 + 8 = 16 = 2^4 or 4^2.
10340 is a term because 10340 + 04301 = 14641 is a perfect power 11^4.

Robert Israel, Table of n, a(n) for n = 1..2000

Cf. A001597, A056964.

filter:= proc(n) local L,i,x;
  L:= convert(n,base,10);
  x:= add(10^(i-1)*L[-i],i=1..nops(L));
  igcd(ifactors(n+x)[2][..,2])>1;
end proc:
select(filter, [$1..20000]); # Robert Israel, Oct 24 2023

isok(k) = ispower(k + fromdigits(Vecrev(digits(k)))); \\ Michel Marcus, Oct 24 2023

More terms from Robert Israel, Oct 24 2023

A371031 Number of distinct integers resulting from adding an n-digit non-multiple of 10 and its reverse.

Original entry on oeis.org

9, 17, 170, 323, 3230, 6137, 61370, 116603, 1166030, 2215457

Offset: 1

César Eliud Lozada, Mar 08 2024

			For n=2 there are 81 2-digit numbers not ending with 0: {11, 12, 13, ..., 99}. There are 17 distinct results when adding each of these to their reversal: {22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198}. Therefore a(2) = 17.

Cf. A056964, A067251, A358985.

A371031[n_] :=
Module[{nn, ss},
  nn = Select[Range[If[n == 1, 1, 10^(n - 1) + 1], 10^n - 1], Mod[#, 10] > 0 &];
  ss = Map[# + FromDigits[Reverse[IntegerDigits[#]]] &, nn];
  Return[CountDistinct[ss]]
];
Map[A371031[#]&, Range[7]]

For n > 1, empirically a(n+1) = 10 a(n) if n even, 19 a(n) / 10 if n odd, and thus a(n+2) = 19 a(n). - Michael S. Branicky, Mar 31 2024

a(9)-a(10) from Michael S. Branicky, Mar 30 2024

A055960 n + reversal of base 11 digits of n (written in base 10).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 60, 72, 84, 96, 108, 120, 132, 144

Offset: 0

Henry Bottomley, Jul 18 2000

If n has an even number of digits in base 11 then a(n) is a multiple of 12.

Cf. A056960, A056964.

Table[n+IntegerReverse[n,11],{n,0,70}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 30 2016 *)

a(n) = n + A056960(n).

A055964 n + reversal of hexadecimal (base 16) digits of n (written in base 10).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238

Offset: 0

Henry Bottomley, Jul 18 2000

If n has an even number of hexadecimal digits then a(n) is a multiple of 17.

Cf. A056962, A056964.

Table[n + IntegerReverse[n, 16], {n, 0, 100}] (* Paolo Xausa, Aug 08 2024 *)

a(n) = n + A056962(n).

A055966 n + reversal of base 20 digits of n (written in base 10).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420

Offset: 0

Henry Bottomley, Jul 18 2000

If n has an even number of base 20 digits then a(n) is a multiple of 21.

Cf. A056964.

a(n) = n + A056963(n).

A247110 n + reversal of digits of n, when n is not palindromic.

Original entry on oeis.org

11, 33, 44, 55, 66, 77, 88, 99, 110, 22, 33, 55, 66, 77, 88, 99, 110, 121, 33, 44, 55, 77, 88, 99, 110, 121, 132, 44, 55, 66, 77, 99, 110, 121, 132, 143, 55, 66, 77, 88, 99, 121, 132, 143, 154, 66, 77, 88, 99, 110, 121, 143, 154, 165, 77, 88, 99, 110, 121, 132, 143, 165, 176, 88, 99, 110, 121, 132, 143, 154, 165, 187, 99, 110, 121

Offset: 10

Morgan L. Owens, Nov 21 2014

Cf. A056964 (n + reversal of digits of n)

With[{n=50}, (FromDigits[#] + FromDigits[Reverse[#]]) & /@ Select[IntegerDigits[Range[n]], # != Reverse[#] &]]
Table[If[n==IntegerReverse[n],Nothing,n+IntegerReverse[n]],{n,100}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 29 2016 *)

A285741 a(0) = 1; a(2n) = a(n), a(2n+1) = a(n) + R(a(n)), where R() is the digit reversal.

Original entry on oeis.org

1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 77, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 77, 4, 8, 8, 16, 8, 16, 16, 77, 8, 16, 16, 77, 16, 77, 77, 154, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 77, 4, 8, 8, 16, 8, 16, 16, 77, 8, 16, 16

Offset: 0

Ilya Gutkovskiy, Apr 25 2017

			a(0) = 1;
a(1) = a(2*0+1) = a(0) + R(a(0)) = 1 + 1 = 2;
a(2) = a(2*1) = a(1) = 2;
a(3) = a(2*1+1) = a(1) + R(a(1)) = 2 + 2 = 4;
a(4) = a(2*2) = a(2) = 2;
a(5) = a(2*2+1) = a(2) + R(a(2)) = 2 + 2 = 4, etc.

Michael Gilleland, Some Self-Similar Integer Sequences
Index entries for sequences related to Reverse and Add!

Cf. A001127 (records), A004086, A056964.

a[0] = 0; a[n_] := If[EvenQ[n], a[n/2], a[(n - 1)/2] + FromDigits[Reverse[IntegerDigits[a[(n - 1)/2]]]] ]; Table[a[n], {n, 0, 90}]

A345338 Integers whose Reverse And Add trajectory reaches its first prime after a record number of iterations (at least one iteration must be performed).

Original entry on oeis.org

1, 5, 181, 10031, 1001320

Offset: 1

Daniel Starodubtsev, Jun 14 2021

a(6) > 10^9 (if it exists).

All numbers whose trajectory reaches a multiple of 3 or 11 before reaching a prime will never reach a prime.

			a(3) = 181 because it takes 3 iterations (181 -> 362 -> 625 -> 1151 (prime)) to reach a prime, which is more than any smaller number.

Cf. A056964.

f(n) = my(t=n, c=1); while(!isprime(t+=fromdigits(Vecrev(digits(t)))), if(gcd(t, 33)>1, return(0)); c++); c;
lista(nn) = my(m); for(k=1, nn, if(f(k)>m, print1(k, ", "); m=f(k))); \\ Jinyuan Wang, Jun 15 2021

from sympy import isprime
def ra(n): s = str(n); return int(s) + int(s[::-1])
def afind(limit):
    record = 0
    for k in range(limit+1):
        m, i = ra(k), 1
        while not isprime(m) and m%3 != 0 and m%11 != 0: m = ra(m); i += 1
        if isprime(m) and i > record: record = i; print(k, end=", ")
afind(1234567) # Michael S. Branicky, Jul 03 2021

A346141 Numbers k whose number of divisors equals the number of divisors in each of R(k), k+R(k), R(k+R(k)), abs(k-R(k)), and R(abs(k-R(k))), where R(m) is the digit reversal of m and where the reversals of m do not equal m.

Original entry on oeis.org

117858, 129138, 137976, 138222, 194838, 201569, 222831, 281256, 302844, 439415, 448203, 454016, 500638, 514934, 516378, 526486, 533938, 552926, 560766, 562936, 595016, 607499, 607597, 610454, 610595, 629255, 639265, 652182, 654018, 659358, 667065, 679731, 684625, 795706, 810456, 813179

Offset: 1

Scott R. Shannon, Jul 05 2021

There are 324 terms below 50 million. In that range the number of divisors of the terms is 8,12,16,24,32 or 48. The first term with 8 divisors is 129138, the first with 12 is 302844, the first with 16 is 117858, the first with 24 is 138222, the first with 32 is 26739192, and the first with 48 is 19245366.

			117858 is a term as the number of divisors of 117858 = tau(117858) = 16, and this equals tau(R(117858)) = tau(858711) = 16, tau(117858+R(117858)) = tau(976569) = 16, tau(R(117858+R(117858))) = tau(965679) = 16, tau(abs(117858-R(117858))) = tau(740853) = 16, and tau(R(abs(117858-R(117858)))) = tau(358047) = 16.

Cf. A000005, A004086, A346113, A056964, A056965.

Subsequence of A062895.

A351729 a(n) is the least prime that starts a sequence of exactly n primes under the iteration p -> p + reverse(p) + 1.

Original entry on oeis.org

7, 3, 5, 2, 7070879, 700839449, 7700584787999

Offset: 1

Robert Israel, Feb 17 2022

			a(3) = 5 because 5 starts the sequence of 3 primes 5 -> 5+5+1 = 11 -> 11+11+1 = 23, the next iteration 23+32+1 = 56 not being prime.

Cf. A004086, A056964.

rev:= proc(x) local L,i;
L:= convert(x,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
f:= proc(n) option remember;
  local x;
  x:= n + rev(n)+1;
  if isprime(x) then 1+procname(x) else 1 fi
end proc:
W:= Array(1..5):
p:= 1: count:= 0:
while count < 5 do
  p:= nextprime(p);
  v:= f(p);
  if W[v] = 0 then W[v]:= p; count:= count+1 fi
od:
convert(W,list);

With[{s = Array[-1 + Length@ NestWhileList[# + IntegerReverse[#] + 1 &, #, PrimeQ] &, 2^23]}, Array[FirstPosition[s, #][[1]] &, 5]] (* Michael De Vlieger, Feb 17 2022 *)

a(6)-a(7) from Martin Ehrenstein, Mar 05 2022

cp's OEIS Frontend

A366080 Numbers that give a perfect power when added to their reverse.

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A371031 Number of distinct integers resulting from adding an n-digit non-multiple of 10 and its reverse.

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A055960 n + reversal of base 11 digits of n (written in base 10).

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A055964 n + reversal of hexadecimal (base 16) digits of n (written in base 10).

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A055966 n + reversal of base 20 digits of n (written in base 10).

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A247110 n + reversal of digits of n, when n is not palindromic.

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A285741 a(0) = 1; a(2*n) = a(n), a(2*n+1) = a(n) + R(a(n)), where R() is the digit reversal.

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Mathematica

A345338 Integers whose Reverse And Add trajectory reaches its first prime after a record number of iterations (at least one iteration must be performed).

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Python

A346141 Numbers k whose number of divisors equals the number of divisors in each of R(k), k+R(k), R(k+R(k)), abs(k-R(k)), and R(abs(k-R(k))), where R(m) is the digit reversal of m and where the reversals of m do not equal m.

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A285741 a(0) = 1; a(2n) = a(n), a(2n+1) = a(n) + R(a(n)), where R() is the digit reversal.