This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
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.
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
8919 is in the sequence because prime(8919) = 92357 contains a substring of prime digits "2357". 27890 is in the sequence because prime(27980) = 323579 contains a substring of prime digits "2357".
F:= proc(d) local x,y,j;
op(map(numtheory:-pi,sort(convert(select(isprime, {seq(seq(seq(x+10^j*2357+10^(j+4)*y, y=10^(d-j-5)..10^(d-j-4)-1),x=1..10^j-1,2),j=1..d-5),
seq(10^(d-4)*2357+x,x=1..10^(d-4)-1),seq(10^4*x+2357,x=10^(d-5)..10^(d-4)-1)}),list))));
end proc:
350, seq(F(d),d=5..7); # Robert Israel, Nov 29 2017
Select[Range[100000], MemberQ[Partition[IntegerDigits[Prime[#]], 4, 1], {2, 3, 5, 7}] &]
isok(n)=p = prime(n); ret = 0; while (p > 1, if ((p % 10000) == 2357, ret = 1; break); p = floor(p/10);); return (ret); \\ Michel Marcus, Dec 15 2017
a(6) = 71132356 = 8464^2 contains 2, 3, 5, 7, 11 and 13 as substrings and no smaller square has that property.
Do[k = 1; While[! AllTrue[Prime@ Range@ n, StringContainsQ[ToString[k^2], ToString@ #] &], k++]; Print[k^2], {n, 9}] (* Michael De Vlieger, Oct 19 2015, Version 10 *)
The series starts as A054261, but 112357 is followed by 112357 because 13 can be obtained with a subsequence '1','3' which is interrupted by '2'.
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