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%I #32 Feb 08 2022 23:37:28
%S 929573,3070663,5285767,5974249,7810223,9262697,9663683,9700429,
%T 10532453,12968519,19106729,19158221,19579907,21825337,23196157,
%U 24328567,29617897,31181461,31746383,31839427,36438379,36745811,37763641,38585039,38774851,38888137,39600559,45412331,45743483,47500217,47632271,54127231,56242891,59816347
%N Weakly prime numbers in the sense of A158124 but not A050249.
%C A158124: initial digit may not be changed to a zero (and hence give a number with fewer digits).
%C A050249: initial digit may be changed to a zero.
%C For the following values 5, 6, 7, 8, 9, 10 of k, the number of terms < 10^k in this sequence is 0, 1, 8, 72, 589, 4977. - _Jean-Marc Rebert_, Nov 10 2015
%C Intersection of A227916 and A158124. So primes p that give another prime when the first digit is removed, but give a composite number when any one digit is modified in a way that does not change the digit count. - _Jeppe Stig Nielsen_, Jan 16 2022
%H Jean-Marc Rebert, <a href="/A158125/b158125.txt">Table of n, a(n) for n = 1..589</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WeaklyPrime.html">Weakly Prime</a>
%o (PARI) forprime(p=2,10^10,d=digits(p);!isprime(fromdigits(d[2..#d]))&&next();for(k=1,#d,for(j=(k==1),9,d[k]==j&&next();e=d;e[k]=j;isprime(fromdigits(e))&&next(3)));print1(p,", ")) \\ _Jeppe Stig Nielsen_, Jan 16 2022
%Y Cf. A050249, A158124, A227916.
%K nonn,base
%O 1,1
%A _Eric W. Weisstein_, Mar 13 2009
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