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

10010101, 11171777, 11177717, 11313331, 11333131, 11919199, 11919991, 13111333, 13131133, 13131331, 13133311, 13311313, 14441411, 16166611, 16616161, 17111777, 17171177, 17171771, 17177117, 17711717, 17717171

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