[seqfan] Distinct functions(n, p)

юрий герасимов 2stepan at rambler.ru
Fri Oct 26 23:24:28 CEST 2012


Dear SegFans, 

If 
1) A060981 is a(n) = A000040(n)*A000040(n + 1)*...*A000040(2n - 1), 
2) A001223 is a(n) = A000040(n + 1) - A000040(n),
 
then 

3) a(n) = A001223(n)*A001223(n + 1)*...*A001223(2n - 1)/ 2^(n-1) are 1, 2, 4, 8, 24, 72, 72, 432, 648, 1296, 3888, 11664, 31104, 62208, 62208, 290304, 290304, 1451520,..
or  4) primes A000040(n) such that A001223(n) = A001223(2n)*A001223(2n + 1) are 89, a(2) = ?
or  5) primes A000040(n) such that 2*A001223(n) = A001223(2n)*A001223(2n + 1) are 13, 43, 53, 79, 109, 139, 193, 251,..
or  6) primes A000040(n) such that 4*A001223(n) = A001223(2n)*A001223(2n + 1) are 2, 3, 5, 23, 31, 83, 157, 167,  
or  7) smallest r > 0 such that A001223(n)*2^(r - 1) = A001223(2n)*A001223(2n + 1) or 0 if no such k exists are 3, 3, 3, 0, 0, 2, 0, 0, 2, 0, 3, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 3, 1, 0,..
or  8) primes A000040(n) such that A001223(2n)*A001223(2n + 1)/A001223(n) = q are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71, 79, 83, 89, 97, 101,...
 
9) smallest m = (mod k) such that A001223(n)*A001223(n + 1)*...*A001223(2n - 1)*2^k/4^(n - 1) is odd number are  0, 0, 0, 0, 1, 2, 3, 3, 5, 5, 6, 7, 5, 5, 6, 6, 7, 9, 11, 10,.. 
or  10) primes A000040(n) such that m = 0 are 2, 3, 5, 7, a(5) = ?
or  11) primes A000040(n) such that m(n) = m(n + 1) are 2, 3, 5, 17, 23, 41, 47,...

Which sequence (3 or 9) will be useful to publish in the OEIS ? 
Which sequence (4 or 5 or 6 or 7 or 8) will be useful to publish in the OEIS ? 
Which sequence (10 or 11) will be useful to publish in the OEIS ? 
a(5) for sequence 10 ?
Tranks is advance. Juri-Stepan Gerasimov.



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