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 A067317 Numbers k such that 1 + binomial(k,j) is prime for only 2 values of j (0 <= j <= k). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA Numbers k such that A067316(k) = 2. EXAMPLE 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. MATHEMATICA 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]]] PROG (PARI) isok(n) = sum(j=0, n, isprime(1 + binomial(n, j))) == 2; \\ Michel Marcus, Oct 30 2018 CROSSREFS Cf. A067316. Sequence in context: A069119 A261413 A187220 * A349743 A141354 A181106 Adjacent sequences:  A067314 A067315 A067316 * A067318 A067319 A067320 KEYWORD more,nonn AUTHOR Labos Elemer, Jan 15 2002 EXTENSIONS More terms from Jon E. Schoenfield, May 30 2010 a(35)-a(41) from Robert Israel, Mar 09 2020 STATUS approved

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Last modified August 7 16:00 EDT 2022. Contains 355994 sequences. (Running on oeis4.)