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%I #28 Mar 02 2019 02:48:11
%S 113,131,137,173,179,197,311,313,317,373,379,419,431,479,613,617,619,
%T 673,719,797,971,1117,1171,1319,1373,1973,1979,2311,2371,2971,3119,
%U 3137,3719,3797,4111,4373,6113,6131,6173,6197,6719,6737
%N Primes > 100 in which every substring of length 2 is also prime.
%C Minimum number of digits is taken to be 3 as all two-digit primes would be trivial members.
%C From _Robert G. Wilson v_, May 12 2014: (Start)
%C The number of terms below 10^n: 0, 0, 21, 46, 123, 329, 810, 1733, 3985, 9710, ..., .
%C The least term with n digits is: 113, 1117, 11113, 111119, ..., see A090534.
%C The largest term with n digits is: 971, 9719, 97973, 979717, ..., see A242377.
%C The digits 2, 4, 5, 6 and 8 can only appear at the beginning of the prime and the digit 0 never appears. But the digits 1, 3, 7 and 9 can appear anywhere, yet only 1,1 can appear as a pair.
%C \10^n
%C d\ 1&2 3 4 5 6 7 8 9 10 Total % @ 10^10
%C \
%C 1 0 19 34 146 648 1162 2678 8037 22740 39.188034
%C 2 0 0 3 6 27 18 66 175 449 0.816186
%C 3 0 14 19 63 326 712 1526 3855 11040 19.403018
%C 4 0 3 2 13 54 92 143 384 1031 1.895550
%C 5 0 0 0 9 17 24 45 176 426 0.763995
%C 6 0 4 6 4 24 66 146 233 630 1.224834
%C 7 0 14 20 100 436 907 1980 5442 15421 26.875285
%C 8 0 0 3 6 24 25 37 176 388 0.721797
%C 9 0 9 13 38 157 361 763 1790 5125 9.111301
%C Total 0 63 100 385 1713 3367 7384 20268 57250 100.00000
%C (End)
%H Robert G. Wilson v, <a href="/A069488/b069488.txt">Table of n, a(n) for n = 1..10101</a> (first 1000 terms from Reinhard Zumkeller)
%e 3719 is a term as the three substrings of length 2, i.e., 37, 71 and 19, are all prime.
%t Do[ If[ Union[ PrimeQ[ Map[ FromDigits, Partition[ IntegerDigits[ Prime[n]], 2, 1]]]] == {True}, Print[ Prime[n]]], {n, PrimePi[100] + 1, 500}]
%o (Haskell)
%o a069488 n = a069488_list !! (n-1)
%o a069488_list = filter f $ dropWhile (<= 100) a038618_list where
%o f x = x < 10 || a010051 (x `mod` 100) == 1 && f (x `div` 10)
%o -- _Reinhard Zumkeller_, Apr 07 2014
%Y Cf. A069489 and A069490.
%Y Cf. A010051, subsequence of zeroless primes: A038618.
%K nonn,base
%O 1,1
%A _Amarnath Murthy_, Mar 30 2002
%E Edited, corrected and extended by _Robert G. Wilson v_, Apr 12 2002
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