A297962 Take a prime, convert it to base 2. Remove its most significant digit and its least significant digit; repeat this process. a(n) is the least prime that, in the first n steps of this process, generates n primes.
13, 59, 631, 7039, 64063, 761087, 3619327, 74347519, 1577707519, 22200700927, 1668463173631, 290703062134783, 3413184213843967, 121597545150218239
Offset: 1
Examples
a(1) = 13, because 13 in base 2 is 1101, 10 is the prime 2; and 13 is the least prime with this property. a(2) = 59, because 59 = 111011_2, 1101_2 is the prime 13, 10_2 is the prime 2; and 59 is the least prime with this property. a(3) = 631, because 631 = 1001110111_2, 111011_2 is the prime 59, 1101_2 is the prime 13, 10_2 is the prime 2; and 631 is the least prime with this property.
Programs
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Java
private static BigInteger SearchAn() { BigInteger BIW, BICore; int tN=10; int j3; static final BigInteger BILim = new BigInteger("1000000000"); static final BigInteger BI2 = new BigInteger("2");for (BIW=BI2; BIW.compareTo(BILim)<0; BIW=BIW.add(BI2)) { BICore = BIW; for (j3=1;j3 -
Maple
with(numtheory): P:=proc(q) local a,i,k,n,ok,x; x:=1; for n from 1 to q do for k from x to q do a:=convert(ithprime(k),binary,decimal); ok:=1; for i from 1 to n do a:=trunc(a/10) mod 10^(ilog10(a)-1); if not isprime(convert(a,decimal,binary)) then ok:=0; break; fi; od; if ok=1 then x:=k; print(ithprime(k)); break; fi; od; od; end: P(10^10);
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Mathematica
With[{s = Map[LengthWhile[#, PrimeQ] &@ NestWhileList[((# - 2^Floor@ Log2@ #) - 1)/2 &, #, # > 2 &] &, Prime@ Range[2^18]]}, Map[Prime@ First@ FirstPosition[s, #] &, Range@ Max@ s]] (* Michael De Vlieger, Jan 10 2018 *)
Formula
Let C(p) be the result of removing the MSD and the LSD of a prime p. C(p) = (p - 2^floor(log_2(p)) - 1)/2.
Extensions
a(10)-a(14) from Jon E. Schoenfield, Jan 11 2018
Comments