A007656 -id:A007656 - cp's OEIS frontend

A179301 Number of stable isotopes of element n.

2, 2, 2, 1, 2, 2, 2, 3, 1, 3, 1, 3, 1, 3, 1, 4, 2, 3, 3, 6, 1, 5, 2, 4, 1, 4, 1, 5, 2, 5, 2, 5, 1, 6, 2, 6, 2, 4, 1, 5, 1, 7, 0, 7, 1, 6, 2, 8, 2, 10, 2, 8, 1, 9, 1, 7, 2, 4, 1, 7, 0, 7, 2, 7, 1, 7, 1, 6, 1, 7, 2, 6, 2, 5, 2, 7, 2, 6, 1, 7, 2, 4, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Will Nicholes, Jul 10 2010

nonn

Stable in this context means either theoretically stable (e.g. Hydrogen-1), or technically radioactive but stable for all practical purposes (e.g. Bismuth-209).

Radioactive nuclides with a half-life of 700 million years or greater are included.

Wikipedia, Table of nuclides.

Cf. A058317, A121818, A007656.

a(106)-a(118) (Sg to Uuo) by Jeremy Tan, Oct 24 2013

A058317 Number of neutrons in atoms of the n-th element of the periodic table (for the most abundant isotope).

Original entry on oeis.org

0, 2, 4, 5, 6, 6, 7, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 22, 20, 20, 24, 26, 28, 28, 30, 30, 32, 31, 35, 35, 39, 41, 42, 45, 45, 48, 48, 50, 50, 50, 51, 52, 54, 55, 57, 58, 60, 61, 64, 66, 69, 71, 76, 74, 77, 78, 81, 82, 82, 82, 84, 84, 88, 89, 93, 94, 97, 98, 99, 100, 103

Offset: 1

Labos Elemer, Dec 12 2000

			a(79)=118 because the 79th element is gold, whose only naturally occurring isotope is Au-197, which has 79 protons, 79 electrons and 118 neutrons.

Y. Bentor, Periodic Table: Neutrons, Chemical Elements.com.
M. Winter, The periodic table of the elements, WebElements.

Cf. A007656, A058318.

a(38) updated by Sean A. Irvine, Aug 24 2021

A070217 Numbers not represented by a known atomic weight as given in Francis W. Aston's Nobel lecture in 1922.

Original entry on oeis.org

2, 3, 5, 8, 13, 17, 18, 21, 33, 34, 38

Offset: 1

Robert G. Wilson v, May 07 2002

Francis W. Aston, Mass spectra and isotopes, Nobel Lecture, December 12, 1922. See p. 18.

Cf. A007656.

Stripped data to original list on page 18 of Aston's lecture by Elijah Beregovsky, Aug 15 2020.

A121818 Average of atomic weights of all isotopes of first n elements, rounded to nearest integer.

Original entry on oeis.org

1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 78, 79, 80, 81, 83, 84, 85

Offset: 1

Jonathan Vos Post, Aug 26 2006

This is poorly defined, even with the caveats of A007656, for the highest atomic numbers (with no stable isotopes) and the values given are with respect to Earth, as different planets presumably have slightly different isotopic ratios.

			a(1) = round(1.0080/1) = 1 = mean atomic weight of hydrogen (protium + deuterium + tritium).
a(2) = round((1.0080+4.003)/2) = round(5.011/2) = round(2.5055) = 3.

Cf. A007656, A070217, A121291.

Needs["Miscellaneous`ChemicalElements`"]
Table[ Round[ Sum[ AtomicWeight(AT)Elements[[i]], {i, n}]/n], {n, 111}] (* Robert G. Wilson v, Sep 02 2006 *)

More terms from Robert G. Wilson v, Sep 02 2006

Edited by N. J. A. Sloane, Sep 14 2006

A058318 Number of energy levels in atoms of the n-th element of the periodic table.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Labos Elemer, Dec 12 2000

Run lengths, i.e., how many elements have 1,2,3,4,5,6,7 energy levels, are 2,8,8,18,18,32,26 (see A137583).

			For n=79, element 79 (Gold) has a(79)=6 energy levels (which may have 2,8,18,32,18,1 electrons).

Y. Bentor, Chemical Elements.Com
M. Winter, WebElements Periodic Table.

Cf. A007656, A018227, A058317, A137583, A173592.

seq(i$[2, 8, 8, 18, 18, 32, 32][i], i=1..7); # Michel Lagneau, Apr 03 2024

a(n) = m for s(m-1) < n <= s(m) for m=1..7, where s(m) = A173592(m) and s(0) = 0. - Michel Lagneau, Apr 03 2024

a(106)-a(118) from Michel Lagneau, Apr 03 2024

A121291 Rounded partial sum of atomic weights of first n elements.

Original entry on oeis.org

1, 5, 12, 21, 31, 43, 57, 73, 92, 112, 135, 160, 187, 215, 246, 278, 318, 353, 392, 432, 477, 525, 576, 628, 683, 739, 798, 857, 920, 986, 1055, 1128, 1203

Offset: 1

Jonathan Vos Post, Aug 24 2006

nonn

			a(1) = round(1.0080) = 1 = mean atomic weight of hydrogen (protium + deuterium + tritium).
a(2) = round (1.0080+4.003) = round(5.011) = 5 (heium 4 and rarer helium 3).

Cf. A007656, A070217.

A180638 Phan Thành Nam's upper bound on the number of non-relativistic electrons bound to a nucleus of charge n.

Original entry on oeis.org

4, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 89, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102

Offset: 1

Jonathan Vos Post, Sep 14 2010

From the abstract: "We prove that the maximal number N_c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3.1Z^(1/3).
This improves Lieb's (1984) upper bound N_c < 2Z+1 when Z <= 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, limsup_{Z->infty} N_c/Z <= 1.22."
Note that the published version of the paper, as revisions v2 and v3 on the arXiv, use the stronger bound 1.22Z + 3Z^(1/3) instead, where the constant 1.22 can be improved to 1.21684.... In particular this improves the bound for lithium, aluminium, scandium, chromium, cobalt, zinc, arsenic, krypton, yttrium, zirconium, etc. Asymptotically Seco, Sigal, & Solovej show that the maximum ionization is n + O(n^(5/7)) and it is conjectured that the maximum ionization is n + O(1). - Charles R Greathouse IV, Sep 13 2016

			a(5) = floor(1.22*5 + 3.1*5^(1/3)) = floor(11.40...) = 11, which means that boron (the element with atomic number 5, i.e., with 5 protons) can have no more than 11 bound electrons, which would give it a -6 charge. B^5- has been observed (in Al_3BC) so this bound is reasonably tight. - _Charles R Greathouse IV_, Sep 14 2016

E. H. Lieb and R. Seiringer, The stability of matter in quantum mechanics, Cambridge University Press, 2009.

E. H. Lieb, Bound on the maximum negative ionization of atoms and molecules, Phys. Rev. A 29, 3018-3028 (1984).
Phan Thành Nam, New bounds on the maximum ionization of atoms , Communications in Mathematical Physics 312:2 (2012), pp. 427-445. arXiv:1009.2367 [math-ph]
L. A. Seco, I. M. Sigal, and J. P. Solovej, Bound on the ionization energy of large atoms, Communications in Mathematical Physics 131:2 (1990), pp. 307-315.

Cf. A007656.

A180638 := proc(n) 1.22*n+3.1*n^(1/3) ; floor(%) ; end proc: seq(A180638(n),n=1..100) ; # R. J. Mathar, Oct 06 2010

Table[Floor[1.22 n + 3.1 n^(1/3)], {n, 73}] (* Michael De Vlieger, Dec 23 2015 *)

a(n)=floor(1.22*n+3.1*sqrtn(n,3)) \\ Charles R Greathouse IV, Sep 13 2016

a(n) = floor(1.22*n + 3.1*n^(1/3)).

Reference converted to link, entries checked - R. J. Mathar, Oct 06 2010

A192409 Number of letters in the English name of the n-th element in the periodic table of the elements.

Original entry on oeis.org

8, 6, 7, 9, 5, 6, 8, 6, 8, 4, 6, 9, 9, 7, 10, 6, 8, 5, 9, 7, 8, 8, 8, 8, 9, 4, 6, 6, 6, 4, 7, 9, 7, 8, 7, 7, 8, 9, 7, 9, 7, 10, 10, 9, 7, 9, 6, 7, 6, 3, 8, 9, 6, 5, 7, 6, 9, 6, 12, 9, 10, 8, 8, 10, 7, 10, 7, 6, 7, 9, 8, 7, 8, 8, 7, 6, 7, 8, 4, 7, 8, 4, 7, 8, 8, 5, 8, 6, 8, 7, 12, 7, 9, 9, 9, 6, 9, 11, 11, 7, 11, 8, 10, 13, 7, 10, 7, 7, 10, 12, 11, 11, 8, 9, 9, 11, 10, 9

Offset: 1

Kausthub Gudipati, Jun 30 2011

The names are based on the IUPAC Inorganic Chemistry Division table.
The sequence appears to be not very well defined, concerning the terms (names can change) and number of terms (in June/November 2016 four new names were given to elements number 113, 115, 117 and 118). - M. F. Hasler, Jan 24 2020
The names my change, certainly, but at any given time the sequence is defined by the names in the IUPAC Inorganic Chemistry Division table. - N. J. A. Sloane, Jan 25 2020

			a(1) = 8, because HYDROGEN uses 8 letters.
a(2) = 6, because HELIUM uses 6 letters.
a(3) = 7, because LITHIUM uses 7 letters.
and so on. Note that a(13) = 9, not 8, since the IUPAC spellings are used.

International Union of Pure and Applied Chemistry, Periodic Table of Elements
Herbert Kaesz, The synthesis and naming of elements 110 and beyond Chemistry International 24:2 (2002), p. 7.
W. H. Koppenol, Naming of new elements, Pure and Applied Chemistry 74:5 (2002), pp. 787-791.
Wikipedia, Periodic table

See A007656 for the atomic weights.

Cf. A005589 (letters in name of n), A070273 (letters in names of the planets), A031139 (letters in names of months), A309750 (variant: in alphabetical order).

Length @ Characters @ ElementData[#, "Name"] & /@ Range[118] (* Amiram Eldar, Jan 25 2020, generates all the terms in the data section with two exceptions: a(13) assumes the name "Aluminum" instead of "Aluminium" and a(55) assumes the name "Cesium" instead of "Caesium" *)

a(7), a(32), a(35) corrected and a(51)-a(118) added by Andrew Howroyd, Jan 24 2020

cp's OEIS Frontend

A179301 Number of stable isotopes of element n.

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A058317 Number of neutrons in atoms of the n-th element of the periodic table (for the most abundant isotope).

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A070217 Numbers not represented by a known atomic weight as given in Francis W. Aston's Nobel lecture in 1922.

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A121818 Average of atomic weights of all isotopes of first n elements, rounded to nearest integer.

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A058318 Number of energy levels in atoms of the n-th element of the periodic table.

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A121291 Rounded partial sum of atomic weights of first n elements.

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A180638 Phan Thành Nam's upper bound on the number of non-relativistic electrons bound to a nucleus of charge n.

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A192409 Number of letters in the English name of the n-th element in the periodic table of the elements.

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