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.
%I A344637 #8 May 26 2021 02:32:06 %S A344637 1,1,1,1,2,4,2,1,1,2,2,1,1,1,1,1,3,1,30,1,1 %N A344637 a(n) is the smallest k > 0 such that the number that results from inserting a string of k zeros between all adjacent digits of prime(n) is also prime, or 0 if no such k exists. %C A344637 Is a(26) = 0? Note that prime(26) = 101 and 101 is the largest known prime of the form 10^t + 1. %C A344637 a(A000720(A004022(i))) = 0 for i > 1, i.e., a(n) = 0 if prime(n) is a repunit > 11. %e A344637 For n = 10: prime(10) = 29 and 200009 is the smallest prime obtained by inserting a string of zeros between all adjacent digits, so a(10) = 4. %o A344637 (PARI) eva(n) = subst(Pol(n), x, 10) %o A344637 insert_zeros(num, len) = my(d=digits(num), v=[]); for(k=1, #d-1, v=concat(v, concat([d[k]], vector(len)))); v=concat(v, d[#d]); eva(v) %o A344637 a(n) = my(p=prime(n)); for(k=1, oo, if(ispseudoprime(insert_zeros(p, k)), return(k))) %Y A344637 Cf. A000720, A004022, A306920, A306926. %K A344637 nonn,base,more %O A344637 5,5 %A A344637 _Felix Fröhlich_, May 25 2021