A091079 -id:A091079 - cp's OEIS frontend

A091077 Numbers n which when converted to base 3, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

64, 208, 640, 1936, 5248, 5824, 15616, 17488, 46720, 50752, 52480, 140032, 151840, 157456, 419968, 425152, 455104, 467200, 472384, 1259776, 1276624, 1364896, 1400320, 1417168, 3779200, 3794752, 3831040, 4094272, 4109824, 4199680, 4235968, 4251520

Offset: 1

Chuck Seggelin, Dec 18 2003

Trivial cases are those numbers which upon conversion result in a number which is palindromic (m = reverse(m)), or a palindrome plus trailing zeros such that m = reverse(m)*10^z where z=number of lost zeros. Nontrivial digit loss occurs when a converted number has trailing zeros that drop off when the number is reversed.

			a(1) = 64 because: 64 in base 3 is 2101; 2101 reversed is 1012; 1012 converted back to base 10 is 32 and 64 mod 32 = 0.

C. Seggelin, Numbers Divisible by Digit Permutations. [Broken link]

Cf. A091078 (same in base 4), A091079 (base 5), A091080 (base 6), A091081 (base 7), A091082 (base 8), A091083 (base 9), A031877 (base 10).

isok(n, b=3) = {m = subst(Polrev(digits(n, b)), x, b); if (n % m, return(0));if ((n/m == 1), return (0)); vq = valuation(n, b); if (! vq, return (1)); qq = subst(Polrev(digits(m,b)), x, b); if (n == b^vq*qq, return (0)); return (1);} \\ Michel Marcus, Oct 10 2014

More terms from Michel Marcus, Oct 10 2014

A091078 Numbers n which when converted to base 4, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

Original entry on oeis.org

225, 945, 3825, 15345, 57825, 61425, 230625, 245745, 921825, 968625, 983025, 368, 6625, 3871665, 3932145, 14745825, 14803425, 15483825, 15671025, 15728625, 589826, 25, 59224545, 61932465, 62672625, 62914545

Offset: 1

Chuck Seggelin, Dec 18 2003

Trivial cases are those numbers which upon conversion result in a number which is palindromic (m = reverse(m)), or a palindrome plus trailing zeros such that m = reverse(m)*10^z where z=number of lost zeros. Nontrivial digit loss occurs when a converted number has trailing zeros that drop off when the number is reversed.

			a(1) = 225 because: 225 in base 4 is 3201; 3201 reversed is 1023; 1023 converted back to base 10 is 75 and 225 mod 75 = 0.

C. Seggelin, Numbers Divisible by Digit Permutations. [Broken link]

Cf. A091077 (same in base 3), A091079 (base 5), A091080 (base 6), A091081 (base 7), A091082 (base 8), A091083 (base 9), A031877 (base 10).

/* See A091077 and use PARI script with b=4 */

More terms from Michel Marcus, Oct 10 2014

A091080 Numbers n which when converted to base 6, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

Original entry on oeis.org

980, 1225, 6020, 7525, 36260, 45325, 217700, 272125, 1271060, 1306340, 1588825, 1632925, 7621460, 7838180, 9526825, 9797725, 45723860, 46817540, 47029220, 57154825, 58521925, 58786525

Offset: 1

Chuck Seggelin, Dec 18 2003

Trivial cases are those numbers which upon conversion result in a number which is palindromic (m = reverse(m)), or a palindrome plus trailing zeros such that m = reverse(m)*10^z where z=number of lost zeros. Nontrivial digit loss occurs when a converted number has trailing zeros that drop off when the number is reversed.

			a(1) = 980 because: 980 in base 6 is 4312; 4312 reversed is 2134; 2134 converted back to base 10 is 490 and 980 mod 490 = 0.

C. Seggelin, Numbers Divisible by Digit Permutations. [Broken link]

Cf. A091077 (same in base 3), A091078 (base 4), A091079 (base 5), A091081 (base 7), A091082 (base 8), A091083 (base 9), A031877 (base 10).

/* See A091077 and use PARI script with b=6 */

More terms from Michel Marcus, Oct 10 2014

A091081 Numbers n which when converted to base 7, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

Original entry on oeis.org

36, 288, 1800, 2052, 2304, 12384, 14400, 16416, 86472, 88236, 99072, 100836, 115200, 605088, 619200, 691776, 705888, 806688, 4235400, 4247748, 4323600, 4335948, 4840704, 4853052, 4928904, 4941252, 5534208, 5647104, 29647584, 29746368, 30254400, 30353184

Offset: 1

Chuck Seggelin, Dec 18 2003

Trivial cases are those numbers which upon conversion result in a number which is palindromic (m = reverse(m)), or a palindrome plus trailing zeros such that m = reverse(m)*10^z where z=number of lost zeros. Nontrivial digit loss occurs when a converted number has trailing zeros that drop off when the number is reversed.

			a(1) = 36 because: 36 in base 7 is 51; 51 reversed is 15; 15 converted back to base 10 is 12 and 36 mod 12 = 0.

C. Seggelin, Numbers Divisible by Digit Permutations. [Broken link]

Cf. A091077 (same in base 3), A091078 (base 4), A091079 (base 5), A091080 (base 6), A091082 (base 8), A091083 (base 9), A031877 (base 10).

/* See A091077 and use PARI script with b=7 */

More terms from Michel Marcus, Oct 10 2014

A091082 Numbers n which when converted to base 8, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

Original entry on oeis.org

42, 378, 2625, 2730, 3066, 3402, 3969, 21546, 23625, 24570, 27594, 32193, 170625, 172074, 174762, 191625, 193914, 196602, 221130, 257985, 1346625, 1376298, 1400490, 1535625, 1548666, 1572858, 1769418, 2064321, 10754625, 10922625, 11010090, 11031594, 11184810

Offset: 1

Chuck Seggelin, Dec 18 2003

Trivial cases are those numbers which upon conversion result in a number which is palindromic (m = reverse(m)), or a palindrome plus trailing zeros such that m = reverse(m)*10^z where z=number of lost zeros. Nontrivial digit loss occurs when a converted number has trailing zeros that drop off when the number is reversed.

			a(1) = 42 because: 42 in base 8 is 52; 52 reversed is 25; 25 converted back to base 10 is 21 and 42 mod 21 = 0.

C. Seggelin, Numbers Divisible by Digit Permutations. [Broken link]

Cf. A091077 (same in base 3), A091078 (base 4), A091079 (base 5), A091080 (base 6), A091081 (base 7), A091083 (base 9), A031877 (base 10).

/* See A091077 and use PARI script with b=8 */

More terms from Michel Marcus, Oct 10 2014

A091083 Numbers n which when converted to base 9, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

Original entry on oeis.org

64, 640, 4800, 5248, 5824, 6400, 43680, 46720, 52480, 58240, 393600, 419968, 425152, 467200, 472384, 524800, 3542880, 3779200, 3831040, 4199680, 4251520, 4723840, 31497600, 31886400, 34012288, 34058944, 34437376, 34484032, 37792000, 37838656, 38217088

Offset: 1

Chuck Seggelin, Dec 18 2003

Trivial cases are those numbers which upon conversion result in a number which is palindromic (m = reverse(m)), or a palindrome plus trailing zeros such that m = reverse(m)*10^z where z=number of lost zeros. Nontrivial digit loss occurs when a converted number has trailing zeros that drop off when the number is reversed.

			a(1) = 64 because 64 in base 9 is 71; 71 reversed is 17; 17 converted back to base 10 is 16 and 64 mod 16 = 0.

C. Seggelin, Numbers Divisible by Digit Permutations. [Broken link]

Cf. A091077 (same in base 3), A091078 (base 4), A091079 (base 5), A091080 (base 6), A091081 (base 7), A091082 (base 8), A031877 (base 10).

/* See A091077 and use PARI script with b=9 */

More terms from Michel Marcus, Oct 10 2014

A222816 Numbers k that divide the base-5 reversal of k.

Original entry on oeis.org

8, 48, 144, 208, 248, 744, 1008, 1248, 3744, 5008, 5208, 6048, 6248, 18744, 25008, 26208, 30048, 31248, 90144, 93744, 125008, 126008, 130208, 131208, 150048, 151048, 155248, 156248, 450144, 468744, 625008, 631008, 650208, 656208, 750048, 756048, 775248, 781248

Offset: 1

N. J. A. Sloane, Mar 13 2013

The base-B reversal of k is obtained by writing k in base B and reversing the order of the digits.

			8 in base 5 is 13_5; its reverse is 31_5, which is 16 in base 10, and 8 divides 16, so 8 is in the sequence.

N. J. A. Sloane, Table of n, a(n) for n = 1..57
Leonard F. Klosinski and Dennis C. Smolarski, On the Reversing of Digits, Math. Mag., 42 (1969), 208-210. [Gives a(1)]
N. J. A. Sloane, 2178 And All That, arXiv:1307.0453 [math.NT], 2013; Fib. Quart., 52 (2014), 99-120.
N. J. A. Sloane, 2178 And All That [Local copy]

Cf. A214927, A091079.

Select[Range[10^6],Divisible[s=FromDigits[Reverse@IntegerDigits[#,5],5],#]&&s!=#&] (* Giorgos Kalogeropoulos, Aug 20 2021 *)

isok(n) = (rdn = subst(Polrev(digits(n,  5)), x, 5)) && (rdn != n) && (rdn % n) == 0; \\ Michel Marcus, Oct 10 2014

More terms from Alois P. Heinz, Mar 13 2013

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A091077 Numbers n which when converted to base 3, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

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A091078 Numbers n which when converted to base 4, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

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A091080 Numbers n which when converted to base 6, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

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A091081 Numbers n which when converted to base 7, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

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A091082 Numbers n which when converted to base 8, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

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A091083 Numbers n which when converted to base 9, reversed and converted back to base 10 yield a number m such that n mod m = 0. Cases which are trivial or result in digit loss are excluded.

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A222816 Numbers k that divide the base-5 reversal of k.

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