A122171 Smallest number m such that there are exactly n primes of form m+p for primes p<2m.
1, 4, 6, 10, 12, 18, 38, 74, 40, 24, 68, 30, 36, 54, 72, 100, 134, 78, 60, 66, 102, 96, 84, 114, 238, 90, 132, 266, 126, 220, 368, 174, 156, 120, 150, 380, 204, 180, 222, 258, 288, 276, 682, 234, 530, 264, 324, 252, 306, 240, 490, 210, 372, 270, 402, 728, 408, 650
Offset: 1
Keywords
Examples
a(4)=10 because it is the first followed by 14,16,... such that exactly 4 primes p respectively below 2*10,2*14,2*16,... form 4 other primes respectively of form p+10,p+14,p+16,...[For m=10, the 4 primes below 20 are 3,7,13,19 ; For m=14, the 4 primes below 28 are 3,5,17,23 ; For m=16, the 4 primes below 32 are 3,7,13,31 ; ...]
Programs
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Maple
A122171 := proc(n) local m,p,pgood; m := 0 ; while true do p := 2 ; pgood := 0 ; while p <= 2*m do if isprime(m+p) then pgood := pgood+1 ; fi ; p := nextprime(p) ; od ; if pgood = n then RETURN(m) ; fi ; m := m+1 ; od ; end: for n from 1 to 80 do printf("%d, ",A122171(n)) ; od : # R. J. Mathar, Dec 16 2006
Extensions
More terms from R. J. Mathar, Dec 16 2006
Comments