A077294 -id:A077294 - cp's OEIS frontend

A077293 Partition the concatenation 1234567...of natural numbers into successive strings nontrivially (a(n) is not equal to n) such that the n-th string is a multiple of n.

12, 34, 567, 8, 910, 111213141516, 17181920, 2122232425262728, 293031, 323334353637383940, 41424344454647, 48, 49505152535455565758596061626364, 6566, 676869707172737475, 767778798081828384, 85, 868788

Offset: 1

Amarnath Murthy, Nov 03 2002

a(1) = 12, a(n) = smallest concatenation of next successive natural numbers that is a multiple of n, or 0 if no such concatenation exists.
a(1) = 1 would have given a trivial sequence 1,2,3,4,5....
Every partial concatenation is a left substring of the concatenation of natural numbers.

			a(2) = 34 = 2*17; a(7) = 17181920 = 7*2454560.

Cf. A077294, A088597, A088598.

lista(nn) = {my(k=0, m); for(n=1, nn, m=k++; while(m%n>0 || m==n, m=eval(Str(m, k++))); print1(m, ", ")); } \\ Jinyuan Wang, May 16 2020

a(n) = A077294(n)*n. - Jinyuan Wang, May 16 2020

Corrected and extended by Ray Chandler, Oct 18 2003

A077295 Partition the concatenation 1234567...of natural numbers into successive strings which are even, all different and > 2. (0 never taken as the most significant digit.)

Original entry on oeis.org

12, 34, 56, 78, 910, 1112, 1314, 1516, 1718, 1920, 212, 22, 32, 4, 252, 6, 272, 8, 2930, 3132, 3334, 3536, 3738, 3940, 414, 24, 344, 454, 64, 74, 84, 950, 5152, 5354, 5556, 5758, 5960, 616, 26, 36, 46, 566, 676, 86, 970, 7172, 7374, 7576, 7778, 7980, 818, 28, 38, 48, 58, 68, 788, 8990, 9192, 9394, 9596, 9798, 99100

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A077293, A077294, A077296, A077297, A077298, A077299, A077300, A077301, A077302.

Corrected and extended by Kyle Shearer (kss198(AT)psu.edu), Mar 14 2006
More terms from Franklin T. Adams-Watters, May 30 2006
Offset changed by Sean A. Irvine, May 14 2025

A077296 Partition the concatenation 1234567... of natural numbers into successive strings which are multiples of 3 all different and > 3. (0 never taken as the most significant digit.)

Original entry on oeis.org

12, 345, 6, 78, 9, 1011, 121314, 15, 1617, 18, 1920, 21, 222, 324, 252, 627, 282, 930, 3132, 33, 3435, 36, 3738, 39, 4041, 42, 4344, 45, 4647, 48, 4950, 51, 525, 354, 555, 657, 585, 960, 6162, 63, 6465, 66, 6768, 69, 7071, 72, 7374, 75, 7677, 787980, 81, 828, 384, 858, 687, 888, 990, 9192, 93, 9495, 96, 9798, 99

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A077293, A077294, A077295, A077297, A077298, A077299, A077300, A077301, A077302.

Corrected and extended by Franklin T. Adams-Watters, May 30 2006

Offset changed by Sean A. Irvine, May 14 2025

A077297 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 4, all different and > 4. (0 never taken as the most significant digit.)

Original entry on oeis.org

12, 3456, 789101112, 13141516, 17181920, 212, 2232, 4252, 6272, 8, 29303132, 33343536, 37383940, 41424, 344, 45464, 748, 49505152, 53545556, 57585960, 616, 2636, 4656, 6676, 869707172, 73747576, 77787980, 81828, 384, 85868, 788

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A077293, A077294, A077295, A077296, A077298, A077299, A077300, A077301, A077302.

Corrected and extended by Franklin T. Adams-Watters, May 30 2006

Offset changed by Sean A. Irvine, May 14 2025

A077298 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 5, all different and > 5. (0 never taken as the most significant digit.)

Original entry on oeis.org

12345, 678910, 1112131415, 1617181920, 2122232425, 2627282930, 3132333435, 3637383940, 4142434445, 4647484950, 515, 25, 35, 45, 55, 65, 75, 85, 960, 6162636465, 6667686970, 7172737475, 7677787980, 8182838485, 8687888990

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A077293, A077294, A077295, A077296, A077297, A077299, A077300, A077301, A077302.

More terms from R. J. Mathar, Mar 13 2006
More terms from Kyle Shearer (kss198(AT)psu.edu), Mar 14 2006
Offset changed by Sean A. Irvine, May 14 2025

A077299 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 6, all different and > 6. (0 never taken as the most significant digit.)

Original entry on oeis.org

12, 3456, 78, 9101112, 1314, 15161718, 1920, 21222, 324, 252, 627282, 930, 3132, 33343536, 3738, 39404142, 4344, 45464748, 4950, 51525354, 5556, 57585960, 6162, 636, 4656, 66, 768, 69707172, 7374, 75767778, 7980, 81828, 384, 858, 687888, 990

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A077293, A077294, A077295, A077296, A077297, A077298, A077300, A077301, A077302.

Corrected and extended by R. J. Mathar, Mar 13 2006

Offset changed by Sean A. Irvine, May 14 2025

A077300 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 7, all different and > 7 (0 is never taken as the most significant digit).

Original entry on oeis.org

1234567891011, 12131, 4151, 6171819202122, 2324, 252, 6272, 829303132, 33343536373, 83940414243, 4445, 46474849505, 15253, 5455565758596061626, 364, 6566, 6768697071727374, 7576777879808182838485, 868, 78889909, 192939495

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A077293, A077294, A077295, A077296, A077297, A077298, A077299, A077301, A077302.

More terms from Sam Alexander, Jan 02 2004

Offset changed by Sean A. Irvine, May 14 2025

A077301 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 8, all different and > 8. (0 never taken as the most significant digit.)

Original entry on oeis.org

123456, 789101112, 1314151617181920, 2122232, 42526272, 82930313233343536, 3738394041424, 344, 45464, 74849505152, 5354555657585960, 616, 26364656, 66768, 6970717273747576, 777879808, 1828384, 858687888, 9909192

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A077293, A077294, A077295, A077296, A077297, A077298, A077299, A077300, A077302.

Corrected and extended by R. J. Mathar, Mar 13 2006

Offset changed by Sean A. Irvine, May 14 2025

A077302 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 9, all different and > 9. (0 never taken as the most significant digit.)

Original entry on oeis.org

12345678, 91011121314151617, 18, 1920212223242526, 27, 2829303, 1323, 33435, 36, 3738394041424344, 45, 4647484950515253, 54, 5556575859606, 162, 63, 64656, 66768697071, 72, 7374757677787980, 81, 828, 384858, 687888, 990, 9192939495969798, 99

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A077293, A077294, A077295, A077296, A077297, A077298, A077299, A077300, A077301.

More terms from Ray G. Opao, Oct 21 2004
Corrected by Sune Kristian Jakobsen (suja01(AT)ceus.dk), Oct 01 2007
Offset changed by Sean A. Irvine, May 14 2025

A077303 Partition the concatenation 235711131719232931...of prime numbers into successive strings such that the n-th string is a multiple of n and >n.

Original entry on oeis.org

2, 357111317192, 32931, 3741434753596, 16771737983899710, 110310, 710911312713, 11371391491511571631671731791811911931971992, 11223, 22722923323924125125726326927127728128329330, 7311313317, 33133734734935335936

Offset: 1

Amarnath Murthy, Nov 03 2002

Cf. A033308, A077293, A077294, A077295, A077296, A077297, A077298, A077299, A077300, A077301, A077302.

More terms from Franklin T. Adams-Watters, May 30 2006

Offset changed by Sean A. Irvine, May 14 2025

cp's OEIS Frontend

A077293 Partition the concatenation 1234567...of natural numbers into successive strings nontrivially (a(n) is not equal to n) such that the n-th string is a multiple of n.

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A077295 Partition the concatenation 1234567...of natural numbers into successive strings which are even, all different and > 2. (0 never taken as the most significant digit.)

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A077296 Partition the concatenation 1234567... of natural numbers into successive strings which are multiples of 3 all different and > 3. (0 never taken as the most significant digit.)

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A077297 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 4, all different and > 4. (0 never taken as the most significant digit.)

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A077298 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 5, all different and > 5. (0 never taken as the most significant digit.)

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A077299 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 6, all different and > 6. (0 never taken as the most significant digit.)

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A077300 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 7, all different and > 7 (0 is never taken as the most significant digit).

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A077301 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 8, all different and > 8. (0 never taken as the most significant digit.)

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A077302 Partition the concatenation 1234567...of natural numbers into successive strings which are multiples of 9, all different and > 9. (0 never taken as the most significant digit.)

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A077303 Partition the concatenation 235711131719232931...of prime numbers into successive strings such that the n-th string is a multiple of n and >n.

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