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Rows of Pascal's triangle which contain no terms numerically adjacent to odd primes (the 1's at either end are of course numerically adjacent to the even prime 2).
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%I #11 Aug 23 2021 06:11:06

%S 7,15,31,63,81,127,239,255,470,511,1023,2047,4095

%N Rows of Pascal's triangle which contain no terms numerically adjacent to odd primes (the 1's at either end are of course numerically adjacent to the even prime 2).

%C Apart from the (2^i-1)-th rows, there are no obvious divisibility properties that would explain the coincidence. '1' is the 0th row.

%e The 7th, 15th, 31st, ... (2^i-1)-th rows are all included as Pascal's triangle only contains odd terms, thus all numerically adjacent terms are even.

%o (PARI) for(n=2, 1000, for(k=1, n\2, ok=1; c=binomial(n, k); if(ispseudoprime(c+1)||ispseudoprime(c-1), ok=0; break; )); if(ok,print1(n, ", ")))

%Y Cf. A007318.

%K nonn,more

%O 1,1

%A _Phil Carmody_, Aug 15 2006

%E Offset changed to 1 and a(11)-a(13) from _Jinyuan Wang_, Aug 23 2021