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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 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 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} \\ Joerg Arndt, Mar 07 2015 (PARI) my(A=primes([0, 15]), i=1); until(#A

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Last modified November 16 13:54 EST 2018. Contains 317274 sequences. (Running on oeis4.)