A008460 Take sum of squares of digits of previous term; start with 6.

6, 36, 45, 41, 17, 50, 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

References

• R. Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 83.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100
• Arthur Porges, A set of eight numbers, Amer. Math. Monthly 52 (1945), 379-382.
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A003132 (the iterated map), A003621, A039943, A099645, A031176, A007770, A000216 (starting with 2), A000218 (starting with 3), A080709 (starting with 4), A000221 (starting with 5), A008462 (starting with 8), A008463 (starting with 9), A139566 (starting with 15), A122065 (starting with 74169). - M. F. Hasler, May 24 2009

Programs

Magma

[6, 36, 45, 41, 17, 50, 25, 29, 85] cat &cat[[89, 145, 42, 20, 4, 16, 37, 58]: n in [0..17]]; // Vincenzo Librandi, Jan 29 2013

Mathematica

NestList[Total[IntegerDigits[#]^2]&, 6, 80] (* Vincenzo Librandi, Jan 29 2013 *)

PARI

A008460(n)=[6,36,45,41,17, 50,25,29,85,89, 145,42,20,4,16, 37,58][if(n<18,n,(n-10)%8+10)] \\ M. F. Hasler, May 24 2009

Formula

Periodic with period 8.

a(13+n) = A080709(n). - M. F. Hasler, May 24 2009

Extensions

An erroneous (duplicate) term deleted by M. F. Hasler, May 24 2009