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A061193 Number of digits in n-th even perfect number (A000396).
(Formerly N0213)
2
1, 2, 3, 4, 8, 10, 12, 19, 37, 54, 65, 77, 314, 366, 770, 1327, 1373, 1937, 2561, 2663, 5834, 5985, 6751, 12003, 13066, 13973, 26790, 51924, 66530, 79502, 130100, 455663, 517430, 757263, 841842, 1791864, 1819050, 4197919, 8107892, 12640858, 14471465, 15632458, 18304103, 19616714, 22370543 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The next known values are 25956377, 25674127, 34850340 and 44677235, but these may not be the next terms. [Updated by M. F. Hasler, Nov 28 2017]

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 19.

Martin Gardner, Mathematical Magic Show. Alfred A. Knopf. 1977 p. 165

Paul Hoffman, Archimedes' Revenge. Penguin. 1988 p. 11

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Donald D. Spencer, Key Dates in Number Theory History. Camelot Pub.Co. 1995 p. 80.

LINKS

Table of n, a(n) for n=1..45.

A. Byerley, Relationship Between Mersenne Primes and Perfect Numbers

C. K. Caldwell, Table of Known Mersenne Primes

C. K. Caldwell, Table of Known Mersenne Primes.

J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]

J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]

J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]

H. J. Smith, Mersenne Primes

FORMULA

a(n) = ceiling((2*A000043(n)-1)*A007524), with A000043 = Mersenne prime exponents, A007524 = log_10(2). - M. F. Hasler, Nov 28 2017

PROG

(PARI) apply( p->(2*p-1)*log(2)\log(10)+1, A000043) \\ where A000043 is the vector of the known Mersenne primes. - M. F. Hasler, Nov 28 2017

CROSSREFS

Cf. A000396.

Sequence in context: A161494 A296161 A121612 * A180941 A190896 A135772

Adjacent sequences:  A061190 A061191 A061192 * A061194 A061195 A061196

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane. This was in the 1973 "Handbook", but was then dropped from the database. Resubmitted by Lekraj Beedassy, May 30 2001.

EXTENSIONS

More terms from Harry J. Smith, Apr 16 2003

Entry revised by N. J. A. Sloane, Jun 10 2012

a(39) through a(45) from M. F. Hasler, Nov 28 2017

STATUS

approved

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Last modified February 19 11:04 EST 2018. Contains 299330 sequences. (Running on oeis4.)