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A237600 Right-truncatable primes in base 16. 12
2, 3, 5, 7, 11, 13, 37, 41, 43, 47, 53, 59, 61, 83, 89, 113, 127, 179, 181, 191, 211, 223, 593, 599, 601, 607, 659, 661, 691, 701, 757, 761, 853, 857, 859, 863, 947, 953, 977, 983, 991, 1427, 1429, 1433, 1439, 1811, 1823, 2039, 2879, 2897, 2903, 2909, 3061 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers with these properties: (i) a(n) is a prime and (ii) its image under the endomorphism E(k)-> k\16 = floor(k/16) has the same properties. The sequence has 414 nonzero members.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..414

Stanislav Sykora, PARI/GP scripts for genetic threads

EXAMPLE

a(414) = 16778492037124607, in hexadecimal notation 3B9BF319BD51FF, belongs to a(n) because each of its hexadecimal prefixes (including itself) is a prime. Being the largest of such numbers, it is also a member of A023107.

MATHEMATICA

Select[Range@ 3600, AllTrue[Most[DeleteDuplicates@ FixedPointList[f, #]], PrimeQ] &] (* Michael De Vlieger, Mar 07 2015, Version 10 *)

PROG

(PARI) GT_Trunc1(nmax, prop, b=10) = { \\ See the link for details

  my (n=0, v=vector(nmax), g=1, lgs=1, lge, an, c);

  for (k=1, b-1, if (prop(k), v[n++]=k));

  lge=n; c=lge-lgs+1;

  while (c, g++; for (k=lgs, lge, for (m=0, b-1, an=b*v[k]+m;

    if (prop(an), v[n++]=an; if (n>=nmax, return (v))); ); );

    lgs=lge+1; lge=n; c=lge-lgs+1; );

  if (n, return (v[1..n]));

  print("No solution"); }

v = GT_Trunc1(1000000, isprime, 16)

(PARI) isok(n) = { while(n, if(!isprime(n), return(0)); n\=16); 1; }

for(n=2, 10^9, if(isok(n), print1(n, ", "))); \\ Joerg Arndt, Mar 07 2015

(Python)

from gmpy2 import is_prime

A237600_list = []

for n in range(1, 10**9):

....if is_prime(n):

........s = format(n, 'x')

........for i in range(1, len(s)):

............if not is_prime(int(s[:-i], 16)):

................break

........else:

............A237600_list.append(n) # Chai Wah Wu, Apr 16 2015

CROSSREFS

Cf. A023107, A024770 (base 10), A237601, A237602, A254756.

Sequence in context: A187614 A191077 A262377 * A228199 A128292 A140464

Adjacent sequences:  A237597 A237598 A237599 * A237601 A237602 A237603

KEYWORD

nonn,base,fini,full

AUTHOR

Stanislav Sykora, Feb 15 2014

STATUS

approved

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Last modified May 26 03:22 EDT 2017. Contains 287073 sequences.