A069570 -id:A069570 - cp's OEIS frontend

A069571 Numbers n in which the k-th digit (counted from the right) is nonzero and is either a divisor of k (but not 1 in case k has a single-digit prime divisor) or a multiple of k, for all 1 <= k <= number of digits of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 22, 23, 24, 25, 26, 27, 28, 29, 41, 42, 43, 44, 45, 46, 47, 48, 49, 61, 62, 63, 64, 65, 66, 67, 68, 69, 81, 82, 83, 84, 85, 86, 87, 88, 89, 321, 322, 323, 324, 325, 326, 327, 328, 329, 341, 342, 343, 344, 345, 346, 347, 348, 349, 361, 362

Offset: 1

Amarnath Murthy, Mar 24 2002

This is the subsequence of terms of A069570 with no digit 1 elsewhere than (possibly) in positions k with no prime divisor < 10, i.e., k = 1, 11, 13, 17, 19, ..., 11*11, 127, 131, 137, 139, 11*13, .... - M. F. Hasler, Sep 27 2016

			54647 is a member but 14647 and 44647 are not members.
13 is a member of A069570 because both 1 and 3 are nonzero, further, 3 is divisible by n = 1 and 1 divides n = 2. 13 is not a member of this sequence because it has a single-digit multiple 3 > 1.
Numbers with "1" in place n = 1 may be in the sequence since 1 divides itself, and 1 does not exceed 1.
21 is a member of this sequence because the digits are nonzero, 1 divides n = 1 and 2 divides n = 2.

Cf. A069570.

Select[Range@ 400, Times @@ Map[Boole, MapIndexed[If[Or[#1 == 0, And[First@ #2 > 1, #1 == 1]], False, Total@ Boole@ {First@ Divisible[#2, #1], First@ Divisible[#1, #2]} > 0] &, Reverse@ IntegerDigits@ #]] > 0 &] (* Michael De Vlieger, Sep 28 2016 *)

Definition clarified by M. F. Hasler, Sep 27 2016

Edited by N. J. A. Sloane, Oct 02 2016

A069559 Triangular numbers in which the k-th significant digit either divides k or is a multiple of k.

Original entry on oeis.org

1, 3, 6, 15, 21, 28, 45, 66, 325, 666, 946, 1128, 1326, 2145, 2346, 2628, 2926, 4186, 8128, 8385, 8646, 8911, 11325, 11628, 14365, 18145, 18915, 51681, 52326, 54615, 54946, 58311, 111628, 118341, 152628, 214185, 258121, 614386, 1152921, 1211346

Offset: 1

Amarnath Murthy, Mar 22 2002

If the smallest prime divisor of n is > 7 then the n-th digit is 1.

			8646 is a member in which the fourth digit is 8 a multiple of 4, the third one is 6 a multiple of 3, the second one is 4 a multiple of 2 and the least significant digit is 6.

Intersection of A000217 and A069570.

Cf. A069556, A069557, A069558.

More terms from Sascha Kurz, Mar 23 2002

Offset changed by Andrew Howroyd, Sep 19 2024

A069560 Squares in which the k-th significant digit either divides k or is a multiple of k.

Original entry on oeis.org

1, 4, 9, 16, 25, 49, 64, 81, 121, 144, 169, 324, 361, 625, 961, 1369, 1681, 2116, 2916, 4624, 8649, 11664, 12321, 14161, 14641, 51984, 114921, 151321, 214369, 311364, 351649, 1151329, 1252161, 1658944, 7311616, 7354944, 41254929, 41654116

Offset: 1

Amarnath Murthy, Mar 22 2002

If the smallest prime divisor of n is > 7 then the n-th digit is 1.

a(65) if it exists is > 10^50. - Andrew Howroyd, Sep 20 2024

			8649 is a member in which the fourth digit is 8 a multiple of 4, the third one is 6 a multiple of 3, the second one is 4 a multiple of 2 and the least significant digit is 9.

Andrew Howroyd, Table of n, a(n) for n = 1..64

Intersection of A000290 and A069570.

Cf. A069556, A069557, A069558, A069559.

isok(k)={my(d=digits(k)); for(i=1, #d, my(t=d[#d+1-i]); if(!t || (t%i && i%t), return(0))); 1}
for(k=1, 10000, my(x=k^2); if(isok(x), print1(x, ", "))) \\ Andrew Howroyd, Sep 19 2024

\\ faster program
B(k)={
  local(L=List());
  my(v=vector(k, i, select(t->t%i==0||i%t==0, [1..9])));
  my(chk(d)=for(i=1, #d, if(!vecsearch(v[i], d[#d+1-i]), return(0)));1);
  my(s=k\2, b=10^s);
  my(recurse(i,m)=if(i==s,
     for(j=sqrtint(m*b+b\10-1)+1, sqrtint(m*b+b-1), my(t=j^2); if(chk(digits(t%b)), listput(L,t))),
    m*=10; foreach(v[i], t, self()(i-1, m+t))
  ));
  recurse(k, 0);
  Vec(L);
}
concat(vector(12,k,B(k))) \\ Andrew Howroyd, Sep 19 2024

More terms from Sascha Kurz, Mar 23 2002

Offset changed by Andrew Howroyd, Sep 19 2024

A069572 Smallest n-digit number in which the k-th digit (from the right!) is a divisor of k, greater than 1 unless k has no single-digit divisor > 1.

Original entry on oeis.org

1, 21, 321, 2321, 52321, 252321, 7252321, 27252321, 327252321, 2327252321, 12327252321, 212327252321, 1212327252321, 21212327252321, 321212327252321, 2321212327252321, 12321212327252321, 212321212327252321

Offset: 1

Amarnath Murthy, Mar 24 2002

Cf. A069570, A069571.

a(12) corrected by Martin Ward, Feb 12 2013

A069573 Largest n-digit number in which the k-th digit is a divisor or a multiple of k.

Original entry on oeis.org

9, 89, 989, 8989, 58989, 658989, 7658989, 87658989, 987658989, 5987658989, 15987658989, 615987658989, 1615987658989, 71615987658989, 571615987658989, 8571615987658989, 18571615987658989, 918571615987658989

Offset: 1

Amarnath Murthy, Mar 24 2002

Cf. A069570, A069571, A069572.

A069574 Smallest n-digit prime in which the k-th digit is a divisor or a multiple of k, or 0 if no such prime exists.

Original entry on oeis.org

2, 11, 113, 1117, 11113, 111119, 1111169, 11111117, 111111113, 1111111121, 11111111113, 111111111149, 1111111111183, 11111111111123, 111111111111389, 1111111111111123, 11111111111111119, 111111111111111143, 1111111111111111111, 11111111111111111143

Offset: 1

Amarnath Murthy, Mar 24 2002

0's are not permitted within the primes. - Sean A. Irvine, May 05 2024

Sean A. Irvine, Table of n, a(n) for n = 1..100

Cf. A069570, A069571, A069572, A069573.

More terms from Sean A. Irvine, May 05 2024

A178843 Numbers in which the n-th digit is either a divisor or a nonzero multiple of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 16, 18, 21, 22, 24, 26, 28, 31, 32, 34, 36, 38, 41, 42, 44, 46, 48, 51, 52, 54, 56, 58, 61, 62, 64, 66, 68, 71, 72, 74, 76, 78, 81, 82, 84, 86, 88, 91, 92, 94, 96, 98, 111, 113, 116, 119, 121, 123, 126, 129, 141, 143, 146, 149, 161, 163

Offset: 1

Jeremy Gardiner, Jun 17 2010

			321 is in the sequence because (counting digits from the left) 3 is a multiple of 1, 2 is a multiple of 2, and 1 is a divisor of 3.

Cf. A069570.

cp's OEIS Frontend

A069571 Numbers n in which the k-th digit (counted from the right) is nonzero and is either a divisor of k (but not 1 in case k has a single-digit prime divisor) or a multiple of k, for all 1 <= k <= number of digits of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A069559 Triangular numbers in which the k-th significant digit either divides k or is a multiple of k.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A069560 Squares in which the k-th significant digit either divides k or is a multiple of k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

PARI

Extensions

A069572 Smallest n-digit number in which the k-th digit (from the right!) is a divisor of k, greater than 1 unless k has no single-digit divisor > 1.

Views

Author

Keywords

Crossrefs

Extensions

A069573 Largest n-digit number in which the k-th digit is a divisor or a multiple of k.

Views

Author

Keywords

Crossrefs

A069574 Smallest n-digit prime in which the k-th digit is a divisor or a multiple of k, or 0 if no such prime exists.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A178843 Numbers in which the n-th digit is either a divisor or a nonzero multiple of n.

Views

Author

Keywords

Examples

Crossrefs