A230638 -id:A230638 - cp's OEIS frontend

A230634 Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly two solutions.

17, 19, 21, 34, 36, 38, 51, 53, 55, 65, 67, 70, 72, 82, 84, 86, 99, 101, 103, 116, 118, 120, 130, 132, 135, 137, 147, 149, 151, 164, 166, 168, 181, 183, 185, 195, 197, 200, 202, 212, 214, 216, 229, 231, 233, 246, 248, 250, 257, 261, 262, 263, 267, 274, 276, 278, 291, 293, 295, 308, 310, 312, 322, 324, 327, 329, 339

Offset: 1

N. J. A. Sloane, Oct 30 2013

Donovan Johnson, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

Related base-4 sequences: A053737, A230631, A230632, A010064, A230633, A230634, A230635, A230636, A230637, A230638, A010065 (trajectory of 1)

etsQ[n_]:=Count[#+Total[IntegerDigits[#,4]]&/@Range[n-1],n]==2; Select[ Range[ 350],etsQ] (* Harvey P. Dale, May 25 2016 *)

A230635 Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly three solutions.

Original entry on oeis.org

16385, 16387, 16402, 16404, 32770, 32772, 32787, 32789, 49155, 49157, 49172, 49174, 65542, 65554, 81922, 81924, 81939, 81941, 98307, 98309, 98324, 98326, 114692, 114694, 114709, 114711, 131079, 131091, 147459, 147461, 147476, 147478, 163844, 163846, 163861

Offset: 1

N. J. A. Sloane, Oct 30 2013

Donovan Johnson, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

Related base-4 sequences: A053737, A230631, A230632, A010064, A230633, A230634, A230635, A230636, A230637, A230638, A010065 (trajectory of 1)

A230636 Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly four solutions.

Original entry on oeis.org

16777234, 33554451, 50331668, 83886099, 100663316, 117440533, 150994964, 167772181, 184549398, 218103829, 234881046, 251658263, 268435476, 268435478, 285212691, 301989908, 318767125, 352321556, 369098773, 385875990, 419430421, 436207638, 452984855, 486539286

Offset: 1

Donovan Johnson and N. J. A. Sloane, Oct 31 2013

Donovan Johnson, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

Related base-4 sequences: A053737, A230631, A230632, A010064, A230633, A230634, A230635, A230636, A230637, A230638, A010065 (trajectory of 1)

A230867 Smallest number m such that u + (sum of base-5 digits of u) = m has exactly n solutions.

Original entry on oeis.org

0, 6, 26, 632, 1953134, 30517578152

Offset: 1

N. J. A. Sloane, Nov 05 2013

Indices of records in A230866: a(n) is the index of the first n in A230866.

The next two terms are a(7) = 5^165 + 27, a(8) = 5^317 + 633.

			a(5) = 1953134 corresponds to the five solutions:
1953099 (base-5: 444444344)
1953103 (base-5: 444444403)
1953105 (base-5: 444444410)
1953129 (base-5: 1000000004)
1953131 (base-5: 1000000011).

Pontus von Brömssen, Table of n, a(n) for n = 1..8 (based on comment about a(7) and a(8))
Max Alekseyev, Table of expressions for a(n), for n=1..100
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.

A230868 gives the leading power of 5 in a(n).
Smallest number m such that u + (sum of base-b digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064.
Cf. A230865, A230866.

a(5) corrected by Donovan Johnson, Nov 05 2013

A238840 Smallest number m such that u + (sum of base-6 digits of u) = m has exactly n solutions.

Original entry on oeis.org

0, 37, 10077697, 2821109907494

Offset: 1

N. J. A. Sloane, Mar 19 2014

The next term is a(5) = 6^((6^9+6^2+8)/5) + 38 = 6^2015548 + 38 and is too large to display.

Max Alekseyev, Table of expressions for a(n), for n=1..100
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.

Smallest number m such that u + (sum of base-b digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064.

A238841 Smallest number m such that u + (sum of base-7 digits of u) = m has exactly n solutions.

Original entry on oeis.org

0, 8, 50, 352, 282475258, 232630513987258, 418377847259091645147530834859099334519176045887014771594

Offset: 1

N. J. A. Sloane, Mar 19 2014

Max Alekseyev, Table of expressions for a(n), for n=1..100
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.

Smallest number m such that u + (sum of base-b digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064.

A238842 Smallest number m such that u + (sum of base-8 digits of u) = m has exactly n solutions.

Original entry on oeis.org

0, 65, 8589934593, 1152921504606847042

Offset: 1

N. J. A. Sloane, Mar 19 2014

The next term is a(5) = 8^((8^11+76)/7) + 66 = 8^1227133524 + 66 and is too large to display.

Max Alekseyev, Table of expressions for a(n), for n=1..100
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.

Smallest number m such that u + (sum of base-b digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064.

A238843 Smallest number m such that u + (sum of base-9 digits of u) = m has exactly n solutions.

Original entry on oeis.org

0, 10, 82, 740, 282429536492, 109418989131512359292, 193632597890512706847971583764083347958511186984324587565465147107798425867049291402906445603076812

Offset: 1

N. J. A. Sloane, Mar 19 2014

Max Alekseyev, Table of expressions for a(n), for n=1..100
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.

Smallest number m such that u + (sum of base-b digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064.

cp's OEIS Frontend

A230634 Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly two solutions.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A230635 Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly three solutions.

Views

Author

Keywords

Links

Crossrefs

A230636 Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly four solutions.

Views

Author

Keywords

Links

Crossrefs

A230867 Smallest number m such that u + (sum of base-5 digits of u) = m has exactly n solutions.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A238840 Smallest number m such that u + (sum of base-6 digits of u) = m has exactly n solutions.

Views

Author

Keywords

Comments

Links

Crossrefs

A238841 Smallest number m such that u + (sum of base-7 digits of u) = m has exactly n solutions.

Views

Author

Keywords

Links

Crossrefs

A238842 Smallest number m such that u + (sum of base-8 digits of u) = m has exactly n solutions.

Views

Author

Keywords

Comments

Links

Crossrefs

A238843 Smallest number m such that u + (sum of base-9 digits of u) = m has exactly n solutions.

Views

Author

Keywords

Links

Crossrefs