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A237600
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Right-truncatable primes in base 16.
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13
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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
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OFFSET
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1,1
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COMMENTS
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Numbers with these properties: (i) a(n) is a prime and (ii) its image under the function E(k) = k\16 = floor(k/16) is zero or has the same properties. [Corrected by M. F. Hasler, Nov 07 2018]
The sequence has 414 nonzero members.
Otherwise said, integers p > 0 such that floor(p/16^k) is prime or zero for all k >= 0. One might relax to p >= 0, i.e., include an initial term 0, corresponding to an empty string of digits. The recursive definition can also be used to produce all of the terms, starting with the primes < 16, and adding, for each term of the list, the primes made from appending a digit to that term, i.e., the primes between 16 x that term and 16 more. The sequence can also be seen as a table whose n-th row yields the terms with n digits in base 16: row lengths are A237601 and the last term of row n is A237602(n). - M. F. Hasler, Nov 07 2018
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range@ 3600, AllTrue[Most[DeleteDuplicates@ FixedPointList[f, #]], PrimeQ] &] (* Michael De Vlieger, Mar 07 2015, Version 10 *)
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PROG
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(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} \\ Joerg Arndt, Mar 07 2015
(PARI) my(A=primes([0, 15]), i=1); until(#A<i+=1, A=concat(A, primes([A[i], A[i]+1]*16))); #A237600=A \\ M. F. Hasler, Nov 07 2018
(Python)
from gmpy2 import is_prime
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:
(Python)
from sympy import primerange
p = lambda x: list(primerange(x, x+16)); A237600 = p(0); i=0
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CROSSREFS
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KEYWORD
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nonn,base,fini,full,easy,tabf
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AUTHOR
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STATUS
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approved
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