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A240959 Smallest number that contains the first n primes as substrings. Substrings can go from left to right or right to left. 2
2, 23, 235, 2357, 112357, 113257, 231175, 11325719, 11325719, 11329175, 11329175, 113291735, 3117329145, 11329143715, 411329173475, 3114329173547, 31143291735947, 1132914347167359, 1132914347167359, 1132914347167359, 1132914347167359, 11329143471673597 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Dmitry Kamenetsky, Table of n, a(n) for n = 1..32

Dmitry Kamenetsky, Results for larger n.

FORMULA

a(n) = A054261(n) for n=1 to 6.

EXAMPLE

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.

PROG

(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

CROSSREFS

Cf. A054261.

Sequence in context: A098739 A287353 A091762 * A054261 A019518 A048677

Adjacent sequences:  A240956 A240957 A240958 * A240960 A240961 A240962

KEYWORD

nonn,base

AUTHOR

Dmitry Kamenetsky, Aug 04 2014

EXTENSIONS

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

STATUS

approved

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Last modified February 19 18:22 EST 2019. Contains 320327 sequences. (Running on oeis4.)