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4, 593, 20494, 266497, 1969376, 10125649, 40473658, 134483969, 387958492, 1001010001, 2359733894, 5162787073, 10609354744, 20668614737, 38454800626, 68736319489, 118612097588, 198393407569, 322734873982, 512064160001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A(3,n) = 3rd 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 a(n) is prime for n = 2, 6, 8, 20, 52. 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(2,n) = 2nd row of semiprime power sum array = A123656. 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
| a(n) = 1+n^4+n^6+n^9 = 1001010001 (base n).
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CROSSREFS
| Cf. A001358, A002523, A091940, A123177, A123656-A123665.
Sequence in context: A102201 A102204 A086143 * A195580 A069641 A079103
Adjacent sequences: A123654 A123655 A123656 * A123658 A123659 A123660
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 04 2006
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