A172035 Smallest exponent k > 1 that sum of digits of k-th power of the n-th prime is a prime (n=1,2,...) or 0 if no such k exists.
5, 0, 2, 2, 9, 3, 2, 5, 3, 2, 7, 2, 4, 5, 2, 2, 5, 2, 3, 6, 2, 2, 2, 2, 4, 8, 4, 2, 2, 4, 2, 8, 2, 3, 2, 2, 4, 4, 6, 2, 4, 2, 10, 3, 4, 2, 3, 2, 4, 3, 5, 6, 3, 4, 4, 2, 2, 2, 2, 2, 3, 4, 3, 3, 3, 5, 3, 3, 8, 2, 3, 12, 2, 3, 2, 5, 2, 3, 8, 16, 8, 3, 4, 2, 3, 2, 4, 2, 2, 5, 7, 4, 3, 8, 3, 2, 6, 2, 3, 6, 2, 2, 10
Offset: 1
Examples
sod(2^5)=5, sod(5^2)=7, sod(7^2)=13, sod(11^9)=53, sod(13^3)=19, sod(17^2)=19, sod(19^5)=37, sod(23^3)=17, sod(29^2)=13, sod(31^7)=31, sod(37^2)=19, sod(41^4)=31, sod(43^5)=31, sod(47^2)=13, sod(53^2)=19, sod(59^5)=47, sod(61^2)=13, sod(67^3)=19, sod(71^6)=37, sod(73^2)=19, sod(79^2)=13, sod(83^2)=31, sod(89^2)=19, sod(97^4)=43, sod(101^8)=67, sod(103^4)=31, sod(107^2)=19, sod(109^2)=19, sod(113^4)=31, sod(127^2)=19, sod(131^8)=61, sod(137^2)=31, sod(139^3)=37, sod(149^2)=7, sod(151^2)=13, sod(157^4)=31, sod(163^4)=37, sod(167^6)=73, sod(173^2)=31, sod(179^4)=37, sod(181^2)=19, sod(191^10)=97, sod(193^3)=37, sod(197^4)=37, sod(199^2)=19, sod(211^3)=37, sod(223^2)=31, sod(227^4)=43, sod(229^3)=37.
References
- M. Fujiwara, Y. Ogawa: Introduction to truly beautiful Mathematics, Chikuma Shobo, Tokyo 2005.
- Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005.
- Hans Schubart: Einfuehrung in die klassische und moderne Zahlentheorie, Vieweg, Braunschweig 1974.
Crossrefs
Cf. A172216. - Klaus Brockhaus, Jan 29 2010
Programs
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Magma
S:=[ 5, 0 ]; for n in [3..103] do j:=2; while not IsPrime(&+Intseq(NthPrime(n)^j)) do j+:=1; end while; Append(~S, j); end for; S; // Klaus Brockhaus, Jan 29 2010
Extensions
More terms from Klaus Brockhaus, Jan 29 2010
Edited by Charles R Greathouse IV, Aug 02 2010
Comments