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 A100813 Smallest number in base 2 which is also prime in base 2+n, or 0 if no such number exists. 1
 10, 11, 10, 11, 10, 111, 1011, 11, 10, 11, 10, 101, 111, 11, 10, 11, 10, 101, 111, 11, 10, 101, 111011, 101, 111, 11, 10, 11, 10, 1011, 111, 10001, 1101, 11, 10, 111, 1011, 11, 10, 11, 10, 1011, 1101, 11, 10, 1011, 1100111, 111, 101001, 11, 10, 101, 111011, 101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 EXAMPLE a(6) = 111: 111 (base 2) = 7, which is prime; 111 (base 2+6) = 73, which is prime. MATHEMATICA a = {}; Do[ k = 1; While[ ! PrimeQ[FromDigits[IntegerDigits[Prime[k], 2], 2 + n]], k++ ]; AppendTo[a, FromDigits[IntegerDigits[Prime[k], 2], 10]]; , {n, 50}]; a (* Ray Chandler, Jan 10 2005 *) PROG (Python) from sympy import isprime, nextprime def fd(s, b): return sum(b**i for i, si in enumerate(s[::-1]) if si=='1') def a(n): p = 2 while not isprime(fd(bin(p)[2:], n+2)): p = nextprime(p) return int(bin(p)[2:]) print([a(n) for n in range(1, 55)]) # Michael S. Branicky, Aug 20 2022 CROSSREFS Sequence in context: A004499 A020509 A103181 * A085209 A085217 A085210 Adjacent sequences: A100810 A100811 A100812 * A100814 A100815 A100816 KEYWORD base,nonn AUTHOR Ray G. Opao, Jan 05 2005 EXTENSIONS Corrected and extended by Ray Chandler, Jan 10 2005 a(51) and beyond from Michael S. Branicky, Aug 09 2022 STATUS approved

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Last modified May 29 20:46 EDT 2024. Contains 372952 sequences. (Running on oeis4.)