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.
2437 prefixed and followed with a pair of digits from (1,2,3,4,5,6,7,8,9) never yields a prime, e.g., '9'2437'1' = 7 * 37 * 43 * 83.
isA032734 := proc(n) for k from 1 to 9 do for k2 from 1 to 9 do dgs := [k,op(convert(n,base,10)),k2] ; dgsn := add( op(i,dgs)*10^(i-1),i=1..nops(dgs)) ; if isprime(dgsn) then return false; end if; end do: end do: return true; end proc: for n from 1 to 50000 do if isA032734(n) then printf("%d,",n); end if; end do: # R. J. Mathar, Oct 22 2011 filter:= proc(n) local d,i,j; d:= 10^(ilog10(n)+2); not ormap(isprime,[seq(seq(d*i+10*n+j,j=[1,3,5,7,9]),i=1..9)]) end proc: select(filter,[$1..10^5]); # Robert Israel, Jul 07 2016
ok[n_] := With[{id = IntegerDigits[n]}, Select[ Flatten[ Table[ FromDigits[ Join[{j}, id, {k}]], {j, 1, 9}, {k, 1, 9}], 1], PrimeQ, 1] == {}]; A032734 = {}; n = 1; While[n < 50000, If[ok[n], Print[n]; AppendTo[A032734, n]]; n++]; A032734(* Jean-François Alcover, Nov 23 2011 *)
Select[Range[50000],NoneTrue[Flatten[Table[FromDigits[Join[{x}, IntegerDigits[ #],{y}]],{x,9},{y,9}]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 07 2018 *)
is_A032734(n)=p=10^#Str(n*=10);forstep(k=n+p,n+9*p,p,nextprime(k)>k+9 || return);1 \\ M. F. Hasler, Oct 22 2011
from sympy import isprime
def ok(n):
s, fdigs, edigs = str(n), "123456789", "1379"
return not any(isprime(int(f+s+e)) for f in fdigs for e in edigs)
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Sep 05 2022
Select[Range[250],PrimeQ[FromDigits[Join[{3},IntegerDigits[#],{3}]]]&] (* Harvey P. Dale, Apr 18 2012 *)
from sympy import isprime
def ok(n): return isprime(int('3' + str(n) + '3'))
print([k for k in range(220) if ok(k)]) # Michael S. Branicky, Sep 04 2022
55553 prefixed with a digit from (1,2,3,4,5,6,7,8,9) and followed by a digit from ('',1,3,7,9) never yields a prime: '3'55553'_' = 11 x 32323; '2'5620'9' = 3 x 41 x 2083.
# Naive program to test for membership - N. J. A. Sloane, Jan 01 2025: isA032737 := proc(x) local S,y,L1,L2,i,j; L1:=[seq(i,i=1..9)]; L2:=[1,3,7,9]; S:=[x]; for i in L1 do y:=parse(cat(i,x)); S:=[op(S),y]; od: for i in L1 do for j in L2 do y:=parse(cat(i,x,j)); S:=[op(S),y]; od: od: for i in S do if isprime(i) then return('false', i,"is prime"); break; fi; od: 'true'; end;
pfdQ[n_]:=CompositeQ[n]&&NoneTrue[Flatten[Table[10(d1*10^IntegerLength[n]+n)+d2,{d1,Range[9]},{d2,{1,3,7,9}}]],PrimeQ] && NoneTrue[ Flatten[Table[d1*10^IntegerLength[n]+n,{d1,Range[9]}]],PrimeQ]; Select[Range[61000],pfdQ] (* Harvey P. Dale, Jan 01 2025 *)
11111 prefixed and followed with a digit from (1,2,3,4,5,6,7,8,9) never yields a prime: '2'11111'3' = 29 x 72797.
60806 prefixed with a digit from ('',1,2,3,4,5,6,7,8,9) and followed by a digit from (1,3,7,9) never yields a prime: '_'60806'3' = 43 x 79 x 179; '1'14612'3' = 3^3 x 11 x 17 x 227.
104609 prefixed or followed by a digit from ('',1,2,3,4,5,6,7,8,9) never yields a prime: '_'104609'_' = 73 x 1433; '8'104609'3' = 3089 x 26237.
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