

A035244


Smallest number with exactly n prime substrings.


49



1, 2, 13, 23, 113, 137, 373, 1137, 1733, 1373, 11317, 11373, 13733, 31373, 113173, 131373, 137337, 337397, 1113173, 1137337, 1373373, 2337397, 3733797, 11373137, 11373379, 13733797, 37337397, 111373379, 123733739
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OFFSET

0,2


COMMENTS

No leading 0's allowed in substrings.
The sequence is welldefined in that for each n the set of numbers with n prime substrings is not empty. Proof by induction: '1' has 0 prime substrings and '2' has 1 prime substring. Let m be a number with n prime substrings. Then 10m+2 is a number with n+1 prime substrings (since m and 10m have identical prime substrings, and '2' is one additional prime substring, but 10m+2 cannot be prime).  Hieronymus Fischer, Aug 26 2012


LINKS



FORMULA



EXAMPLE

a(4)=113 since 3, 11, 13 and 113 are prime and no smaller number works.


MATHEMATICA

f[n_] := Block[{s = IntegerDigits[n], c = 0, d = {}}, l = Length[s]; t = Flatten[ Table[ Take[s, {i, j}], {i, 1, l}, {j, i, l}], 1]; k = l(l + 1)/2; While[k > 0, If[ t[[k]][[1]] != 0, d = Append[d, FromDigits[ t[[k]] ]]]; k ]; Count[ PrimeQ[d], True]]; a = Table[0, {25}]; Do[ b = f[n]; If[ a[[b + 1]] == 0, a[[b + 1]] = n], {n, 1, 15000000}]; a


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



