cp's OEIS Frontend

A173002 Primes consisting of two digits only, each digit with frequency f = 4.

%I A173002 #6 Aug 03 2013 06:20:23
%S A173002 10010101,11171777,11177717,11313331,11333131,11919199,11919991,
%T A173002 13111333,13131133,13131331,13133311,13311313,14441411,16166611,
%U A173002 16616161,17111777,17171177,17171771,17177117,17711717,17717171
%N A173002 Primes consisting of two digits only, each digit with frequency f = 4.
%C A173002 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
%C A173002 2 digits, f = 2: no primes as abab has divisor 101, abba and aabb divisor 11
%C A173002 2 digits, f = 3: no primes as sum of digits 3 * (a+b)
%C A173002 2 digits, f = 4: there are 18 possibilities for (a,b):
%C A173002 (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)
%C A173002 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
%D A173002 Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005
%D A173002 Wladyslaw Narkiewicz: The development of prime number theory: from Euclid to Hardy and Littlewood, Springer Monographs in Mathematics, Berlin, New York, 2000
%D A173002 Paulo Ribenboim: The little book of bigger primes, Springer Berlin, New York, 2004
%e A173002 Complete list classified according to the 18 possible "pairs":
%e A173002 10010101, 10011101
%e A173002 11313331, 11333131, 13111333, 13131133, 13131331, 13133311, 13311313, 31133131, 33113131
%e A173002 14441411, 41414411, 44114141
%e A173002 16166611, 16616161, 61116661, 61661161, 66161611
%e A173002 11171777, 11177717, 17111777, 17171177, 17171771, 17177117, 17711717, 17717171, 71117177, 71171717, 71717117, 77111717, 77711171
%e A173002 11919199, 11919991, 19111999, 19199119, 19911919, 19991911, 91919911, 91999111, 99111919, 99119191, 99919111
%e A173002 23223323, 32323223
%e A173002 22929299, 29229929, 29299229, 29992229, 92922299, 99292229
%e A173002 34434343, 44334343, 44343433
%e A173002 35553533, 53355353, 53533553
%e A173002 33373777, 33773737, 37373773, 37377337, 73337377, 73337773, 73373737, 73773373, 77337373, 77733373
%e A173002 38383883, 88838333
%e A173002 47447747, 77474447
%e A173002 44994949, 49444999, 49494499, 49499449, 94449499
%e A173002 55599959, 99555959
%e A173002 67766767, 76767667
%e A173002 77997979, 79779979, 79797997, 79997977, 99977797, 99979777
%e A173002 88989899, 98988899, 98989889, 99898889
%Y A173002 A087511, A087512, A087513, A087514, A087515, A087527, A087528, A087529, A087530, A087531, A087532, A087533, A087534, A087535, A087536, A087537, A087538
%K A173002 base,fini,nonn
%O A173002 1,1
%A A173002 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 07 2010
%E A173002 Second entry 10011101 deleted (does not comply with definition) and a new term added at the end. _Lekraj Beedassy_, Jul 17 2010