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A301806
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Numbers k such that the concatenation of 2^k - 1 and 2^(k - 1) - 1 is prime.
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1
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2, 3, 4, 7, 8, 12, 19, 22, 36, 46, 51, 67, 79, 215, 359, 394, 451, 1323, 2131, 3336, 3371, 6231, 19179, 39699, 51456, 56238, 69660, 75894, 79798, 92020, 174968, 176006, 181015, 285019, 331259, 360787, 366770
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OFFSET
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1,1
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COMMENTS
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541456 is a term. - Paolo Galliani, Feb 12 2020
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LINKS
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Table of n, a(n) for n=1..37.
MathOverflow, Probable primes of a particular form.
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EXAMPLE
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2 is in the sequence because the concatenation of 3 and 1 is 31, which is prime.
3 is in the sequence because the concatenation of 7 and 3 is 73, which is prime.
5 is not in the sequence because the concatenation of 31 and 15 is 3115 = 5 * 7 * 89.
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MATHEMATICA
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Select[Range[10^3], PrimeQ@ FromDigits[Join @@ IntegerDigits@ {2^# - 1, 2^(# - 1) - 1}] &] (* Michael De Vlieger, Oct 17 2018 *)
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PROG
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(PFGW) ABC2 (2^$a-1)*10^len(2^($a-1)-1)+2^($a-1)-1 a: from x to y
(PARI) isok(n) = isprime(eval(concat(Str(2^n-1), Str(2^(n-1)-1)))); \\ Michel Marcus, Mar 27 2018
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CROSSREFS
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Cf. A000040, A000225, A298613 (associated primes).
Sequence in context: A051213 A340111 A211659 * A066847 A057887 A202116
Adjacent sequences: A301803 A301804 A301805 * A301807 A301808 A301809
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KEYWORD
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nonn,base,more
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AUTHOR
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Paolo Galliani, Mar 27 2018
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EXTENSIONS
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a(33) from Paolo Galliani, May 02 2018
a(34) from Paolo Galliani, Jun 14 2018
a(35) from Paolo Galliani, Jul 17 2018
a(36)-a(37) from Paolo Galliani, Aug 27 2018
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STATUS
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approved
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