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A280539
Numbers k such that the number of partitions of k contains k as a substring.
1
1, 2, 3, 37, 47, 67, 87, 98, 252, 274, 450, 468, 556, 618, 662, 731, 789, 847, 866, 950, 971, 990, 1154, 1163, 1590, 1800, 1851, 1954, 1959, 2073, 2240, 2775, 2999, 3095, 3234, 3520, 3816, 3848, 3986, 4193, 4497, 4541, 4557, 4661, 4710, 4815, 4982, 5123, 5220
OFFSET
1,2
COMMENTS
Number of partitions of a(n) ending in a(n) are 1, 2, 3, 37, 8745, ...
LINKS
EXAMPLE
Number of partitions of 37 is 21637, and 37 is a substring.
Number of partitions of 468 is 380095468763120598477, and 468 is a substring.
MAPLE
with(combinat): P:=proc(q) local a, b, k, n; for n from 1 to q do
a:=numbpart(n); b:=ilog10(n)+1; for k from 1 to ilog10(numbpart(n))+1-ilog10(n) do
if n=a mod 10^b then print(n); break; fi; a:=trunc(a/10); od; od; print(); end: P(50000);
MATHEMATICA
Select[Range[6000], SequenceCount[IntegerDigits[PartitionsP[#]], IntegerDigits[#]]>0&] (* Harvey P. Dale, Oct 22 2022 *)
CROSSREFS
Cf. A000041.
Sequence in context: A355236 A340845 A266758 * A216145 A109748 A062459
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jan 05 2017
STATUS
approved