A061205 -id:A061205 - cp's OEIS frontend

A001128 Reverse digits of previous term and multiply by previous term.

2, 4, 16, 976, 662704, 269896807264, 124883600543123110859968, 108643488775144622666209173128243503963147630528

Offset: 1

John Cerkan, Table of n, a(n) for n = 1..12

a[n_]:=If[n<2, 2,a[n - 1] * FromDigits[Reverse[IntegerDigits[a[n - 1]]]]]; Table[a[n], {n, 10}] (* Indranil Ghosh, Mar 18 2017 *)

a(n) = if (n==1, 2, prev = a(n-1); prev*fromdigits(Vecrev(digits(prev)))); \\ Michel Marcus, Mar 18 2017

def a(n): return 2 if n<2 else a(n - 1) * int(str(a(n - 1))[::-1]) # Indranil Ghosh, Mar 18 2017

a(n) = A061205(a(n-1)) for n>1, with a(1) = 2. - Michel Marcus, Mar 18 2017

A073041 n*R(n)-1 is prime, where R(n) is reverse of n.

Original entry on oeis.org

2, 12, 21, 30, 36, 60, 63, 90, 114, 132, 150, 162, 174, 192, 198, 204, 231, 237, 240, 246, 255, 261, 264, 291, 306, 330, 360, 378, 390, 402, 411, 420, 438, 447, 456, 462, 471, 477, 495, 510, 552, 588, 594, 603, 609, 627, 630, 642, 654, 669, 690, 726, 732

Offset: 1

Shyam Sunder Gupta, Aug 23 2002

From Robert Israel, Jul 25 2019: (Start)
If n is in the sequence and is not divisible by 10, then A004086(n) is in the sequence.
All terms except 2 are divisible by 3. (End)

			12 is a term because 12*21-1=251 is prime.

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

Cf. A004086, A061205.

revdigs:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
select(t -> isprime(t*revdigs(t)-1), [$1..1000]); # Robert Israel, Jul 25 2019

Select[Range[800],PrimeQ[# IntegerReverse[#]-1]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 05 2020 *)

A270926 Numbers k such that k*R(k) can be represented as the sum of two nonzero squares, where R(k) is the reverse of the decimal expansion of k.

Original entry on oeis.org

5, 10, 15, 16, 18, 20, 25, 30, 37, 40, 50, 51, 52, 55, 58, 60, 61, 70, 73, 78, 80, 81, 85, 87, 89, 90, 98, 100, 101, 104, 106, 109, 110, 111, 122, 125, 128, 145, 146, 148, 149, 150, 159, 160, 162, 164, 165, 168, 169, 174, 176, 180, 181, 192, 195, 198, 200, 202, 208, 212, 220, 221, 222

Offset: 1

Soumil Mandal, Mar 26 2016

k*R(k) is the square of the hypotenuse of a right triangle.

Palindromes in this sequence are 5, 55, 101, 111, 181, 202, 212, 222, 232, 272, 292, 303, 313, 323, 333, 353, 373, ... - Altug Alkan, Mar 26 2016

			For k=5, R(k)=5 and k*R(k)=25, which is 3^2 + 4^2.
For k=10, R(k)=1 and k*R(k)=10, which is 1^2 + 3^2.
For k=58, R(k)=85 and k*R(k)=4930, which is 13^2 + 69^2.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A000404, A004086, A061205.

Select[Range@ 222, Length[PowersRepresentations[# FromDigits@ Reverse@ IntegerDigits@ #, 2, 2] /. {0, } -> Nothing] > 0 &] (* _Michael De Vlieger, Mar 26 2016 *)
stnzsQ[{a_,b_}]:=AllTrue[{a,b},IntegerQ[Sqrt[#]]&]; Select[Range[ 250], Length[ Select[IntegerPartitions[#  IntegerReverse[#],{2}],stnzsQ]] >0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 12 2020 *)

isA000404(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
lista(nn) = for(n=1, nn, if(isA000404(n*eval(concat(Vecrev(Str(n))))), print1(n, ", "))); \\ Altug Alkan, Mar 26 2016

# Soumil Mandal, Mar 27 2016
def isHypotenuse(num):
    a, b = 1, 1
    a2, b2 = a**2, b**2
    while a2 + b2 <= num:
        while a2 + b2 <= num:
            if a2 + b2 == num:
                return True
            b += 1
            b2 = b**2
        a += 1
        a2 = a**2
        b = 1
        b2 = b**2
    return False
for x in range(20000):
    if isHypotenuse(x * int(str(x)[::-1])):
        print(x)

More terms from Altug Alkan, Mar 26 2016

A277258 Numbers such that n+R(n) | n*R(n), where R(n) is the digits reverse of n.

Original entry on oeis.org

2, 4, 6, 8, 22, 44, 66, 88, 110, 132, 198, 202, 212, 220, 222, 231, 232, 242, 252, 262, 264, 272, 282, 292, 297, 330, 396, 404, 414, 424, 434, 440, 444, 454, 462, 464, 474, 484, 494, 495, 550, 594, 606, 616, 626, 636, 646, 656, 660, 666, 676, 686, 693, 696, 770

Offset: 1

Paolo P. Lava, Oct 07 2016

This sequence contains all positive terms of A029951. So the sequence is infinite. - Altug Alkan, Oct 07 2016

			R(132) = 231, (132 * 231) / (132 + 231) = 30492 / 363 = 84.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A004086, A029951, A056964, A061205, A131058.

R:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end: P:= proc(q) local n; for n from 1 to q do if type(n*R(n)/(n+R(n)),integer) then print(n); fi; od; end: P(10^4);

Select[Range@ 770, Function[r, Mod[# r, # + r] == 0]@ FromDigits@ Reverse@ IntegerDigits@ # &] (* Michael De Vlieger, Oct 14 2016 *)

R(n) = eval(concat(Vecrev(Str(n))));
isok(n) = n*R(n) % (n+R(n)) == 0; \\ Michel Marcus, Oct 15 2016

A305131 Numbers k with the property that there exists a positive integer multiplier M such that M times the sum of the digits of k, multiplied further by the reversal of this product, gives k.

Original entry on oeis.org

1, 10, 40, 81, 100, 400, 640, 736, 810, 1000, 1300, 1458, 1729, 1944, 2268, 2430, 3640, 4000, 6400, 7360, 7744, 8100, 10000, 12070, 12100, 13000, 14580, 16120, 17290, 19440, 22680, 23632, 24300, 27010, 30250, 31003, 36400, 38152, 40000, 42282, 51142, 63504

Offset: 1

Viorel Nitica, May 26 2018

These numbers are related to the taxicab number 1729, which has multiplier 1. This is why they might be called "multiplicative Hardy-Ramanujan numbers".

If a(n) is in the sequence, then 10 * a(n) is also in the sequence, with the multiplier 10 times larger. We could call primitive the terms not of this form. Primitive terms which end in 0 are 40, 640, 1300, 2430, 3640, 12070, 12100, 16120, 27010, ... - M. F. Hasler, May 27 2018

			For k = 1729 the sum of the digits is 19 and M = 1: 19 * 91 = 1729.
For k = 122512 the sum of the digits is 13 and M = 31: 13 * 31 = 403 and 403 * 304 = 122512.

Viorel Nitica, About some relatives of the taxicab numbers, arXiv:1805.10739 [math.NT], 2018; J. of Int. Seq., 21 (2018), Article 18.9.4. [Where these numbers are introduced.]
Viorel Nitica, Andrei Török, About Some Relatives of Palindromes, arXiv:1908.00713 [math.NT], 2019.
Viorel Niţică, Jeroz Makhania, About the Orbit Structure of Sequences of Maps of Integers, Symmetry (2019), Vol. 11, No. 11, 1374.

Subsequence of A005349 (Niven numbers).

Cf. A004086, A011541, A061205, A305130.

select( is(n,s=sumdigits(n))=n&&!frac(n/=s)&&fordiv(n,M,fromdigits(Vecrev(digits(s*M)))*M==n&&return(1)), [0..10^5]) \\ M. F. Hasler, May 27 2018

A116065 Numbers k, not ending in 0, such that k times its digital reverse gives a number made of nontrivial runs of identical digits.

Original entry on oeis.org

88, 385, 583, 1426, 5236, 5929, 6241, 6325, 9295, 284213, 312482, 1001099, 9901001, 15046244, 44264051, 101127144, 176452305, 220741304, 403147022, 441721101, 469671917, 503254671, 719176964, 1110212002, 1111340003, 1315098605, 2002120111, 2024968033, 2433379564

Offset: 1

Giovanni Resta, Feb 13 2006

A run of length 1 is trivial.

			15046244 * 44264051 = 666007711774444.
5236 * 6325 = 33117700.

Cf. A033023, A061205.

okQ[n_]:=Module[{idn=IntegerDigits[n],revnt},revnt=n FromDigits[Reverse[ idn]]; Last[idn]!=0&&Min[Length/@Split[ IntegerDigits[revnt]]]>1]; Select[Range[10^6],okQ] (* Harvey P. Dale, Jan 04 2012 *)

Corrected and extended by Giovanni Resta, Aug 30 2025

Incorrect comment removed by Jason Yuen, Aug 30 2025

cp's OEIS Frontend

A001128 Reverse digits of previous term and multiply by previous term.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A073041 n*R(n)-1 is prime, where R(n) is reverse of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A270926 Numbers k such that k*R(k) can be represented as the sum of two nonzero squares, where R(k) is the reverse of the decimal expansion of k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Extensions

A277258 Numbers such that n+R(n) | n*R(n), where R(n) is the digits reverse of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A305131 Numbers k with the property that there exists a positive integer multiplier M such that M times the sum of the digits of k, multiplied further by the reversal of this product, gives k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A116065 Numbers k, not ending in 0, such that k times its digital reverse gives a number made of nontrivial runs of identical digits.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions