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A344860 Numbers k such that A306920(k) contains the digit 0 and A306920(k+1) is not A306920(k) with a digit 0 removed.

%I A344860 #11 May 31 2021 21:32:39
%S A344860 192,238,250,293,312,346,382,432,436,446,465,510,544,554,560,571,578,
%T A344860 583,593,607,609,631,658,671,727,729,771,780,803,812,825,844,845,848,
%U A344860 860,866,877,883,894,917,945,962,967,974,991,1000,1004,1031,1042,1052,1061
%N A344860 Numbers k such that A306920(k) contains the digit 0 and A306920(k+1) is not A306920(k) with a digit 0 removed.
%e A344860 A306920(192) = 1021, containing the digit 0, A306920(193) = 1039 and 1039 cannot be obtained by removing a 0 digit from 1021, so 192 is a term of the sequence.
%o A344860 (PARI) eva(n) = subst(Pol(n), x, 10)
%o A344860 insert(n, len, pos) = my(d=digits(n), v=[], w=[]); for(y=1, pos, v=concat(v, d[y])); v=concat(v, vector(len)); for(z=pos+1, #d, v=concat(v, d[z])); eva(v)
%o A344860 a306920(n) = forprime(p=10, , for(k=1, #digits(p)-1, my(zins=insert(p, n, k)); if(ispseudoprime(zins), return(p))))
%o A344860 remove_zeros(n) = my(v=[], w=[], d=digits(n)); for(x=1, #d, if(d[x]==0, for(y=1, x-1, w=concat(w, d[y])); for(z=x+1, #d, w=concat(w, d[z]))); if(#w > 0, v=concat(v, [eva(w)])); w=[]); vecsort(v, , 8)
%o A344860 is(n) = my(x=a306920(n), y=a306920(n+1), rz=remove_zeros(x)); if(#setintersect([0], vecsort(digits(x)))==0, return(0)); for(k=1, #rz, if(y==rz[k], return(0))); 1
%Y A344860 Cf. A306920, A306926.
%K A344860 nonn,base
%O A344860 1,1
%A A344860 _Felix Fröhlich_, May 31 2021