cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A349865 Composite numbers that are missing from A349278.

Original entry on oeis.org

25, 26, 34, 38, 39, 46, 49, 51, 57, 58, 62, 68, 69, 74, 75, 76, 82, 85, 86, 87, 92, 93, 94, 95, 102, 106, 111, 114, 115, 116, 118, 119, 121, 122, 123, 124, 125, 129, 133, 134, 138, 141, 142, 143, 145, 146, 147, 148, 152, 155, 158, 159, 161, 164, 166, 169, 171, 172, 174, 177, 178
Offset: 1

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Author

Bernard Schott, Dec 03 2021

Keywords

Comments

Since no prime >= 11 is a term in A349278, only composite numbers are listed here.

Examples

			There does not exist an integer d.u, where . stands for concatenation, such that 26 = u*(u+d), so 26 is a term.
As 28 = A349278(34) = 4*(4+3), 28 is not a term.

Crossrefs

Cf. A349278, A349864.
Equals disjoint union of A349733 and A350061.

Extensions

More terms from Michel Marcus, Dec 04 2021

A349732 Smallest k such that A349194(k) = n, or 0 if no such k exists.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 0, 24, 0, 25, 32, 26, 0, 27, 0, 28, 34, 29, 0, 35, 50, 0, 36, 43, 0, 37, 0, 44, 38, 0, 52, 39, 0, 0, 0, 46, 0, 61, 0, 47, 54, 0, 0, 48, 70, 55, 0, 49, 0, 63, 56, 71, 0, 0, 0, 57, 0, 0, 72, 80, 58, 65, 0, 0, 0, 59, 0, 66, 0, 0, 0, 0, 74, 67, 0, 82, 90
Offset: 1

Views

Author

Bernard Schott, Nov 28 2021

Keywords

Comments

Composite numbers m for which a(m) = 0 are in A349733.

Examples

			a(10) = 19 since 1*(1+9) = 10 and no integer du < 19 gives d*(d+u) = 10.

Crossrefs

Cf. A349194, A349733.

Formula

If p prime >= 11, a(p) = 0.

A350061 Numbers k for which there exists a preimage m_1 such that A349194(m_1) = k but there is no preimage m_2 such that A349278(m_2) = k.

Original entry on oeis.org

25, 49, 75, 125, 147, 242, 245, 343, 363, 375, 484, 605, 625, 676, 726, 845, 847, 968, 1014, 1029, 1089, 1183, 1210, 1225, 1352, 1452, 1521, 1690, 1694, 1715, 1815, 1875, 1936, 2028, 2178, 2312, 2366, 2401, 2420, 2535, 2541, 2601, 2662, 2704, 2890, 3025, 3042, 3125, 3267, 3380
Offset: 1

Views

Author

Bernard Schott, Dec 12 2021

Keywords

Comments

Numbers that can be expressed as the product of the sum of the first i digits of k, as i goes from 1 to the total number of digits of k for some k, but not as the product of the sum of the last i digits of m, with i going from 1 to the total number of digits of m, for any m.
The preimages m_1 are necessarily multiples of 10; the first few are 50, 70, 320, 500, 340, ...
As A349733 is a subsequence of A349865, there are no numbers t for which there exists a preimage m_4 such that A349278(m_4) = t but there is no preimage m_3 such that A349194(m_3) = t.

Examples

			A349194(122) = 1*(1+2)*(1+2+2) = 15 and A349278(23) = 3*(3+2) = 15, hence, 15 is not a term.
A349194(50) = 5*(5+0) = 25 but there is no m_2 such that A349278(m_2) = 25, because 25 = A349865(1), hence 25 is a term.
A349194(340) = 3*(3+4)*(3+4+0) = 147 but there is no m_2 such that A349278(m_2) = 340, because 147 = A349865(47), hence 147 is a term.

Crossrefs

Cf. A349194, A349278.
Equals A349865 \ A349733.

Extensions

a(6)-a(50) from Michel Marcus, Dec 12 2021
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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