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A240053
3rd Arithmetic derivation of products of 2 successive prime numbers (A006094).
2
0, 16, 32, 10, 48, 1, 92, 1, 92, 96, 156, 1, 128, 44, 188, 608, 248, 1408, 22, 1472, 240, 324, 368, 30, 86, 288, 32, 1188, 1, 1552, 30, 560, 476, 2176, 924, 476, 5120, 60, 432, 2176, 1148, 512, 4480, 1, 1300, 324, 1, 391, 1052, 46, 720, 3232, 672, 2304, 1448, 860, 2484, 1036, 226, 768, 7232, 1628
OFFSET
1,2
COMMENTS
The first arithmetic derivation of products of 2 successive prime numbers (A006094) is the sum of 2 successive prime numbers (A001043). A001043 = (A006094)’. The second arithmetic derivation is (A240052) = (A001043)’ = (A006094)’’. The third arithmetic derivation of products of 2 successive prime numbers (A006094) is a(n) = (A240052)’ = (A001043)’’ = (A006094)’’’.
LINKS
Wikipedia, p-derivation
FORMULA
a(n) = (A006094(n))’’’.
a(n) = A099306(A006094(n)).
a(n) = A003415(A240052(n)).
EXAMPLE
a(12)=(A006094(12))'''=(37*41)'''=(A001043(12))''=(78)''=(71)'=1;
a(14)=(A006094(14))'''=(43*47)'''=(A001043(12))''=(90)''=(123)'=44.
MAPLE
with(numtheory); P:= proc(q) local a, b, c, d, n, p; a:=ithprime(n)*ithprime(n+1);
for n from 1 to q do a:=ithprime(n)*ithprime(n+1);
b:=a*add(op(2, p)/op(1, p), p=ifactors(a)[2]); c:=b*add(op(2, p)/op(1, p), p=ifactors(b)[2]);
d:=c*add(op(2, p)/op(1, p), p=ifactors(c)[2]); print(d);
od; end: P(10^4); # Paolo P. Lava, Apr 07 2014
CROSSREFS
Cf. A003415 (1st derivative), A068346 (2nd derivative), A099306 (3rd derivative).
Sequence in context: A265134 A220000 A132299 * A059164 A040240 A296761
KEYWORD
nonn
AUTHOR
Freimut Marschner, Mar 31 2014
STATUS
approved