A077293 -id:A077293 - cp's OEIS frontend

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.)

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

A355790 Numbers that can be written as the product of two divisors greater than 1 such that the number is contained in the string concatenation of the divisors.

Original entry on oeis.org

64, 95, 110, 210, 325, 510, 624, 640, 664, 950, 995, 1010, 1100, 1110, 3250, 3325, 5134, 6240, 6400, 6640, 6664, 7125, 7616, 8145, 9500, 9950, 9995, 11000, 11100, 11110, 20100, 21052, 21175, 25100, 26208, 32500, 33250, 33325, 35126, 50100, 51020, 51204, 51340, 57125, 62400, 64000, 65114

Offset: 1

Scott R. Shannon, Jul 17 2022

			64 is a term as 64 = 16 * 4 and "16" + "4" = "164" contains "64".
65114 is a term as 65114 = 4651 * 14 and "4651" + "14" = "465114" contains "65114".
See the attached text file for other examples.

Scott R. Shannon, Divisor product of the first 232 terms. These are all the numbers up to 50000000.

Cf. A355791 (base-2), A030190, A210959, A027750, A355852, A339144, A341035, A342127, A027748, A048991, A330027, A077293.

from sympy import divisors
def ok(n):
    s, divs = str(n), divisors(n)[1:-1]
    return any(s in str(d)+str(n//d) for d in divs)
print([k for k in range(1, 10**5) if ok(k)]) # Michael S. Branicky, Jul 27 2022

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

A077304 Partition the concatenation 235711131719232931...of prime numbers into successive strings such that the n-th string is a multiple of prime(n) and > prime(n).

Original entry on oeis.org

2357111317192, 32931, 374143475, 35, 961677173798, 38997101, 103107109113127131137139149151157163167173179181191193197199, 211223, 227229233239241, 251257263269, 27127728, 12832933073, 11313317331337

Offset: 1

Amarnath Murthy, Nov 03 2002

a(5)=961677173798 since 961677173798 = prime(5)*87425197618 = 11*87425197618 > 11. - R. Piyo (nagoya314(AT)yahoo.com), Dec 11 2004

Cf. A033308, A077293, A077294, A077295, A077296, A077297, A077298, A077299, A077300, A077301, A077302, A077303.

Corrected by R. Piyo (nagoya314(AT)yahoo.com), Dec 11 2004

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

A077305 Partition the concatenation 468910121415161820212224252627283032... of composite numbers into successive strings such that the n-th string is a multiple of prime(n) and > prime(n).

Original entry on oeis.org

4, 6, 8910, 121415, 161820212224, 25262728303233343, 536383940424445464849505152, 5455565, 758606263, 6465666, 8697072747576777880818, 2848586878890919293949, 59698991001021041051061081101111121141151161171181191201

Offset: 1

Amarnath Murthy, Nov 03 2002

			a(4) = 121415 is a multiple of prime(4) = 7.

Cf. A077293, A077294, A077295, A077296, A077297, A077298, A077299, A077300, A077301, A077302, A077303, A077304.

Cf. A129808.

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

cp's OEIS Frontend

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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A355790 Numbers that can be written as the product of two divisors greater than 1 such that the number is contained in the string concatenation of the divisors.

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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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A077304 Partition the concatenation 235711131719232931...of prime numbers into successive strings such that the n-th string is a multiple of prime(n) and > prime(n).

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A077305 Partition the concatenation 468910121415161820212224252627283032... of composite numbers into successive strings such that the n-th string is a multiple of prime(n) and > prime(n).

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