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Search: id:A123656
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| 3, 81, 811, 4353, 16251, 47953, 120051, 266241, 538003, 1010001, 1786203, 3006721, 4855371, 7567953, 11441251, 16842753, 24221091, 34117201, 47176203, 64160001, 85960603, 113614161, 148315731, 191434753, 244531251, 309372753, 387951931
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OFFSET
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1,1
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COMMENT
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A(2,n) = 2nd row of semiprime power sum array A(k,n) = 1 + SUM[i=1..k]n^semiprime(i) = 1 + SUM[i=1..k]n^A001358(i). If we deem semiprime(0) = 1, the array is A(k,n) = SUM[i=0..k]n^A001358(i). This sequence is prime for a(1) = 3, a(3) = 811, a(30) = 729810001, a(33) = 1292653891. A(1,n) = first row of semiprime power sum array = 1+n^4 = A002523(n) = 10001(base n). Primes in the first row are A091940. A(3,n) = 3rd row of semiprime power sum array is A123657. A(4,n) = 4th row of semiprime power sum array is A123658. A(5,n) = 5th row of semiprime power sum array is A123659. A(6,n) = 6th row of semiprime power sum array is A123659. A(21,n) = 21st row of semiprime power sum array is A123665 whose polynomial is surprisingly reducible over Z and thus prime-free. A(n,n) = A123177 Main diagonal of semiprime power sum array.
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FORMULA
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a(n) = 1+n^4+n^6 = 1010001 (base n).
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CROSSREFS
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Cf. A001358, A002523, A091940, A123177, A123657-A123665.
Sequence in context: A074386 A116009 A068562 this_sequence A060851 A116179 A013732
Adjacent sequences: A123653 A123654 A123655 this_sequence A123657 A123658 A123659
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 04 2006
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