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A242265 Primes that become composite numbers if the most significant digit is removed. 2
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 (list; graph; refs; listen; history; text; internal format)
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 qualifies because 127 is prime but 27 is composite. 131 does not qualify 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

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Last modified December 4 17:50 EST 2021. Contains 349526 sequences. (Running on oeis4.)