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A240959
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Smallest number that contains the first n primes as substrings. Substrings can go from left to right or right to left.
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3
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2, 23, 235, 2357, 112357, 113257, 231175, 11325719, 11325719, 11329175, 11329175, 113291735, 3117329145, 11329143715, 411329173475, 3114329173547, 31143291735947, 1132914347167359, 1132914347167359, 1132914347167359, 1132914347167359, 11329143471673597
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OFFSET
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1,1
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COMMENTS
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In this version substrings can go from left to right or right to left. The version that only allows substrings to go from left to right is A054261.
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LINKS
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FORMULA
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EXAMPLE
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a(7) = 231175, because 231175 is the smallest number that contains the first 7 primes as substrings: 2, 3, 5, 7, 11 and 13. Note that number 13 is contained from right to left.
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PROG
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(PARI) allss(d, ss, nbc) = {for (i=1, nbc, for (j=1, #d -i +1, subd = []; subd = concat(subd, d[j]); for (k=1, i-1, subd = concat(subd, d[j+k]); ); ss = vecsort(concat(ss, subst(Pol(subd), x, 10)), , 8); ); ); return (ss); }
isoks(k, n, vp) = {nbc = #Str(prime(n)); d = digits(k); sd = vecsort(d, , 8); for (j=1, #vp, if (!vecsearch(sd, vp[j]), return(0)); ); ss = []; if (#d < nbc, return(0)); ss = allss(d, ss, nbc); rd = vector(#d, i, d[#d - i +1]); ss = allss(rd, ss, nbc); for (i=1, n, if (! vecsearch (ss, prime(i)), return (0)); ); return (1); }
a(n) = {vp = []; for (i=1, n, dp = digits(prime(i)); for (k=1, #dp, vp = vecsort(concat(vp, dp[k]), , 8); ); ); k = subst(Pol(vp), x, 10); while (!isoks(k, n, vp), k++); k; } \\ Michel Marcus, Aug 28 2014
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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The author says he is not 100% certain that the later terms are correct, and would appreciate an independent verification. - N. J. A. Sloane, Sep 04 2014
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STATUS
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approved
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