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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 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.)