A242265 Primes that become composite numbers if the most significant digit is removed.

19, 29, 59, 79, 89, 109, 127, 139, 149, 151, 157, 163, 181, 191, 193, 199, 227, 233, 239, 251, 257, 263, 269, 277, 281, 293, 349, 409, 421, 433, 439, 449, 457, 463, 487, 491, 499, 509, 521, 557, 563, 569, 577, 587, 593, 599, 677, 691, 709, 727, 733, 739, 751

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) ~ n log n. - Charles R Greathouse IV, May 11 2014

Example

127 is a term because 127 is prime but 27 is composite.
131 is not a term because 131 and 31 are both prime.

Maple

a:= proc(n) option remember; local p, m;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         m:= irem(p, 10^(length(p)-1));
         if m>1 and not isprime(m) then return p fi
      od
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 10 2014

Mathematica

Select[Prime[Range[5, 200]], PrimeOmega[FromDigits[Drop[IntegerDigits[#], 1]]] > 1 &] (* Alonso del Arte, May 10 2014 *)
Select[Prime[Range[200]], CompositeQ[FromDigits[Rest[IntegerDigits[ #]]]]&] (* Harvey P. Dale, Mar 09 2016 *)

Prog

(Sage)
[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
(PARI) drop(v)=v[2..#v];
iscomposite(n)=n>3 && !isprime(n);
is(n)=isprime(n) && n>9 && iscomposite(subst(Pol(drop(digits(n))), 'x, 10)) \\ Charles R Greathouse IV, May 11 2014

Crossrefs

Sequence in context: A062679 A106093 A084666 * A004618 A030433 A242550

Adjacent sequences: A242262 A242263 A242264 * A242266 A242267 A242268

Keyword

nonn,base

Author

J. Lowell, May 09 2014

Status

approved