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A067317
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Numbers k such that 1 + binomial(k,j) is prime for only 2 values of j (0 <= j <= k).
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2
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1, 3, 7, 15, 23, 31, 59, 63, 67, 81, 84, 93, 95, 127, 157, 170, 214, 239, 253, 255, 313, 470, 511, 622, 694, 1010, 1023, 1098, 1691, 2047, 3535, 3836, 3963, 4095, 6143, 7166, 8191, 11757, 12525, 12686, 16383, 32767
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OFFSET
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1,2
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LINKS
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FORMULA
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Numbers k such that A067316(k) = 2.
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EXAMPLE
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The 2 values of j are 0 and n, which give the prime 2. The sequence includes all numbers of the form 2^m-1 since binomial(2^m-1,j) is odd for all j.
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MATHEMATICA
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test[n_] := Module[{}, For[i=1, 2i<=n, i++, If[PrimeQ[Binomial[n, i]+1], Return[False]]]; True]; For[n=1, True, n++, If[test[n], Print[n]]]
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PROG
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(PARI) isok(n) = sum(j=0, n, isprime(1 + binomial(n, j))) == 2; \\ Michel Marcus, Oct 30 2018
(PARI) is(n) = if(n == 1, 1, for(i=1, n\2, if(isprime(binomial(n, i) + 1), return(0))); 1); \\ Amiram Eldar, Jul 18 2024
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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