

A113515


If the name of the nth Pope is Pope XXX the kth, then the nth term is k.


2



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

1,24


COMMENTS

The apparent inconsistency that a(n) has its second "3" before its second "2" is due to the ambiguous nomenclature of Pope(48) = "St. Felix III (II)" [A.D. 483492], Pope(54) = "St. Felix IV (III)" [A.D. 526530], et cetera, as well as Pope(77) = "Adeodatus (II)" [A.D. 672676]. Pope(140) = "Sylvester II" [9991003], also known as Gerbert, was the greatest mathematician among all popes [see D.E. Smith]. Note also that the generally superb Catholic Encyclopedia differs with independent sources on matters such as periods of time with no pope and periods with two or even three simultaneous popes.  Jonathan Vos Post, Jan 14 2006


REFERENCES

D. E. Smith, History of mathematics  Vol. 1: General survey of the history of elementary mathematics (Boston, 1923), pp. 195196.


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..266
Catholic Encyclopedia, List of Popes
Kevan Choset, in The Volokh Conspiracy, A puzzle
J. V. Post, Timeline 11th Century.


EXAMPLE

In Jan 2006 the current Pope, the 266th (according to the standard enumeration), is Benedict XVI, so a(266) = 16.


CROSSREFS

Cf. A106806.
Sequence in context: A087102 A194309 A318829 * A103754 A058665 A327103
Adjacent sequences: A113512 A113513 A113514 * A113516 A113517 A113518


KEYWORD

nonn,fini


AUTHOR

N. J. A. Sloane, Jan 13 2006. This version of the sequence originated in Kevan Choset's posting of Jan 12 2006 (see link).


STATUS

approved



