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Search: id:A106734
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| 1, 1, 13, 43, 97, 181, 301, 463, 673, 937, 1261, 1651, 2113, 2653, 3277, 3991, 4801, 5713, 6733, 7867, 9121, 10501, 12013, 13663, 15457, 17401, 19501, 21763, 24193, 26797, 29581, 32551, 35713, 39073, 42637, 46411, 50401, 54613, 59053, 63727
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OFFSET
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1,3
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COMMENT
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n*a(n) + n*(n - 1)*7 = n^4.
After the two units, there are 23 consecutive prime or semiprime values. See notes on primes in another cubic, A105551. Primes in this cubic include: a(3) = 13, (4) = 43, a(5) = 97, a(6) = 181, a(8) = 463, a(9) = 673, a(10) = 937, a(13) = 2113, a(17) = 4801, a(19) = 6733, a(20) = 7867, a(22) = 10501, a(26) = 17401, a(27) = 19501, a(31) = 29581, a(36) = 46411, a(39) = 59053, a(40) = 63727. Semiprimes include a(7) = 301 = 7 * 43, a(11) = 1261 = 13 * 97, a(12) = 1651 = 13 * 127, a(14) = 2653 = 7 * 379, a(15) = 3277 = 29 * 113, a(16) = 3991 = 13 * 307, a(18) = 5713 = 29 * 197, a(21) = 9121 = 7 * 1303, a(23) = 12013 = 41 * 293, a(24) = 13663 = 13 * 1051, a(28) = 21763 = 7 * 3109, a(30) = 26797 = 127 * 211, a(29) = 24193 = 13 * 1861, a(32) = 32551 = 43 * 757, a(33) = 35713 = 71 * 503, a(34) = 39073 = 41 * 953, a(35) = 42637 = 7 * 6091, a(37) = 50401 = 13 * 3877, a(38) = 54613 = 13 * 4201. There are no 3-almost primes until a(25) = 15457 = 13 * 29 * 41. - Jonathan Vos Post (jvospost3(AT)gmail.com), May 16 2005
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EXAMPLE
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a(2) = 1, 1 + 15 = 2^4; a(3) = 13, 13 + 27 + 41 = 3^4; a(4) = 43, 43 + 57 + 71 + 85 = 4^4
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CROSSREFS
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Cf. A105551.
Sequence in context: A132233 A031382 A082040 this_sequence A066465 A023262 A067260
Adjacent sequences: A106731 A106732 A106733 this_sequence A106735 A106736 A106737
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KEYWORD
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nonn
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AUTHOR
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Andras Erszegi (erszegi.andras(AT)chello.hu), May 14 2005
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 16 2007
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