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%I #39 Jun 09 2022 21:55:36
%S 19,29,59,79,89,109,127,139,149,151,157,163,181,191,193,199,227,233,
%T 239,251,257,263,269,277,281,293,349,409,421,433,439,449,457,463,487,
%U 491,499,509,521,557,563,569,577,587,593,599,677,691,709,727,733,739,751
%N Primes that become composite numbers if the most significant digit is removed.
%H Alois P. Heinz, <a href="/A242265/b242265.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) ~ n log n. - _Charles R Greathouse IV_, May 11 2014
%e 127 is a term because 127 is prime but 27 is composite.
%e 131 is not a term because 131 and 31 are both prime.
%p a:= proc(n) option remember; local p, m;
%p p:= `if`(n=1, 1, a(n-1));
%p do p:= nextprime(p);
%p m:= irem(p, 10^(length(p)-1));
%p if m>1 and not isprime(m) then return p fi
%p od
%p end:
%p seq(a(n), n=1..100); # _Alois P. Heinz_, May 10 2014
%t Select[Prime[Range[5, 200]], PrimeOmega[FromDigits[Drop[IntegerDigits[#], 1]]] > 1 &] (* _Alonso del Arte_, May 10 2014 *)
%t Select[Prime[Range[200]],CompositeQ[FromDigits[Rest[IntegerDigits[ #]]]]&] (* _Harvey P. Dale_, Mar 09 2016 *)
%o (Sage)
%o [x for x in primes(1000) if not(is_prime(x-(x.digits(base=10)[-1])*10^(floor(log(x,base=10))))) and x-(x.digits(base=10)[-1])*10^(floor(log(x,base=10)))!=1and x-(x.digits(base=10)[-1])*10^(floor(log(x,base=10)))!=0] # _Tom Edgar_, May 10 2014
%o (PARI) drop(v)=v[2..#v];
%o iscomposite(n)=n>3 && !isprime(n);
%o is(n)=isprime(n) && n>9 && iscomposite(subst(Pol(drop(digits(n))),'x,10)) \\ _Charles R Greathouse IV_, May 11 2014
%K nonn,base
%O 1,1
%A _J. Lowell_, May 09 2014
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