The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by M. F. Hasler (See also M. F. Hasler's wiki page
and changes approved by M. F. Hasler)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A001788

a(n) = n*(n+1)*2^(n-2).
(history; published version)

#221 by M. F. Hasler at Sat Oct 05 11:15:21 EDT 2024

STATUS

editing

proposed

#220 by M. F. Hasler at Sat Oct 05 11:05:51 EDT 2024

DATA

0, 1, 6, 24, 80, 240, 672, 1792, 4608, 11520, 28160, 67584, 159744, 372736, 860160, 1966080, 4456448, 10027008, 22413312, 49807360, 110100480, 242221056, 530579456, 1157627904, 2516582400, 5452595200, 11777605632, 25367150592, 54492397568, 116769423360, 249644974080, 532575944704

PROG

(PARI) A001788_upto(n)=Vec(x/(1-2*x)^3+O(x^n), -n) \\ for illustration. - M. F. Hasler, Oct 05 2024

STATUS

approved

editing

A045503

If decimal expansion of n is ab...d, a(n) = a^a + b^b +...+ d^d.
(history; published version)

#18 by M. F. Hasler at Tue Oct 01 11:15:05 EDT 2024

STATUS

editing

proposed

#17 by M. F. Hasler at Tue Oct 01 11:14:58 EDT 2024

CROSSREFS

Cf. A045512 (excludes zero digits).

STATUS

proposed

editing

A046253

Equal to the sum of its nonzero digits raised to its own power.
(history; published version)

#43 by M. F. Hasler at Tue Oct 01 11:10:07 EDT 2024

STATUS

editing

proposed

#42 by M. F. Hasler at Tue Oct 01 11:10:03 EDT 2024

CROSSREFS

Fixed points of A045512. See also A045503 (including nonzero includes zero digits).

#41 by M. F. Hasler at Tue Oct 01 11:05:41 EDT 2024

COMMENTS

A variant of Munchausen Münchausen numbers. Cf, cf. A166623.

The sequence is finite, because the sum can't exceed 9^9*L < 10^9*L, where L is the number of digits, and for L > 10 this is less than the number N >= 10^(L-1). - M. F. Hasler, Oct 01 2024

LINKS

Geoff Bailey, <a href="https://homepage.kranzky.com/puzzles/power_ultra.c">C program for the sequence</a> (cf. Hutchens link for more info), Aug. 1998

Jason Hutchens, <a href="https://homepage.kranzky.com/puzzles/Power.html">power summation</a> (originally at ciips.ee.uwa.edu.au/~hutch), 1997

PROG

(C) see Bailey and Hutchens links

(PARI) select( {is_A046253(n)=n==A045512(n)}, [0..10^4]) \\ To find the 4th solution, multiply the set by 51817. - M. F. Hasler, Oct 01 2024

CROSSREFS

Fixed points of A045512. See also A045503 (including nonzero digits).

STATUS

approved

editing

Discussion

Tue Oct 01

11:09

M. F. Hasler: Hutchens' program is from 1997, and his web page updated Aug.1998 features Bailey's (undated) program.

A045512

If decimal expansion of n is ab...d, a(n) = a^a + b^b + ... + d^d (ignoring any 0's).
(history; published version)

#19 by M. F. Hasler at Tue Oct 01 10:37:04 EDT 2024

STATUS

editing

proposed

#18 by M. F. Hasler at Tue Oct 01 10:36:57 EDT 2024

PROG

(PARI) apply( {A045512(n)=vecsum([d^d|d<-digits(n), d])}, [0..44]) \\ M. F. Hasler, Oct 01 2024

CROSSREFS

See A046253 for fixed points.

STATUS

approved

editing

A045503

If decimal expansion of n is ab...d, a(n) = a^a + b^b +...+ d^d.
(history; published version)

#16 by M. F. Hasler at Tue Oct 01 10:34:40 EDT 2024

STATUS

editing

proposed