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A173002 Primes consisting of two digits only, each digit with frequency f = 4. 0
10010101, 11171777, 11177717, 11313331, 11333131, 11919199, 11919991, 13111333, 13131133, 13131331, 13133311, 13311313, 14441411, 16166611, 16616161, 17111777, 17171177, 17171771, 17177117, 17711717, 17717171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

2 digits, f = 1: 20 primes p 11 < p < =97: 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

2 digits, f = 2: no primes as abab has divisor 101, abba and aabb divisor 11

2 digits, f = 3: no primes as sum of digits 3 * (a+b)

2 digits, f = 4: there are 18 possibilities for (a,b):

(1,0), (1,3), (1,4), (1,6), (1,7), (1,9), (2,3), (2,9), (3,4), (3,5), (3,7), (3,8), (4,7), (4,9), (5,9), (6,7), (7,9), (8,9)

Each possibility occurs, 2+9+3+5+13+11+2+6+3+3+10+2+2+5+2+2+6+4 = 90 = 2 * 3^2 * 5 primes

REFERENCES

Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005

Wladyslaw Narkiewicz: The development of prime number theory: from Euclid to Hardy and Littlewood, Springer Monographs in Mathematics, Berlin, New York, 2000

Paulo Ribenboim: The little book of bigger primes, Springer Berlin, New York, 2004

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

Complete list classified according to the 18 possible "pairs":

10010101, 10011101

11313331, 11333131, 13111333, 13131133, 13131331, 13133311, 13311313, 31133131, 33113131

14441411, 41414411, 44114141

16166611, 16616161, 61116661, 61661161, 66161611

11171777, 11177717, 17111777, 17171177, 17171771, 17177117, 17711717, 17717171, 71117177, 71171717, 71717117, 77111717, 77711171

11919199, 11919991, 19111999, 19199119, 19911919, 19991911, 91919911, 91999111, 99111919, 99119191, 99919111

23223323, 32323223

22929299, 29229929, 29299229, 29992229, 92922299, 99292229

34434343, 44334343, 44343433

35553533, 53355353, 53533553

33373777, 33773737, 37373773, 37377337, 73337377, 73337773, 73373737, 73773373, 77337373, 77733373

38383883, 88838333

47447747, 77474447

44994949, 49444999, 49494499, 49499449, 94449499

55599959, 99555959

67766767, 76767667

77997979, 79779979, 79797997, 79997977, 99977797, 99979777

88989899, 98988899, 98989889, 99898889

CROSSREFS

A087511, A087512, A087513, A087514, A087515, A087527, A087528, A087529, A087530, A087531, A087532, A087533, A087534, A087535, A087536, A087537, A087538

Sequence in context: A260915 A072144 A087510 * A139120 A210893 A107273

Adjacent sequences:  A172999 A173000 A173001 * A173003 A173004 A173005

KEYWORD

base,fini,nonn

AUTHOR

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 07 2010

EXTENSIONS

Second entry 10011101 deleted (does not comply with definition) and a new term added at the end. Lekraj Beedassy, Jul 17 2010

STATUS

approved

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Last modified May 27 06:24 EDT 2019. Contains 323599 sequences. (Running on oeis4.)