This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
is(n)=vecmax(if((d=Set(digits(n)))[1],d,d=setminus(vector(9,i,i),d)))-vecmin(d)==#d-1
A182781aux := proc(Lhig,n) local lsb,a ; if n = 0 then if isprime(Lhig) then 1; else 0; end if; else a := 0 ; lsb := Lhig mod 10 ; if lsb > 0 then a := a + procname(10*Lhig+lsb-1,n-1) ; end if; if lsb < 9 then a := a + procname(10*Lhig+lsb+1,n-1) ; end if; a; end if; end proc: A182781 := proc(n) if n = 1 then 4; else a := 0 ; for l from 1 to 9 do a := a + A182781aux(l,n-1) ; end do: a ; end if; end proc: # R. J. Mathar, Feb 01 2011
a207954 n = a207954_list !! (n-1) a207954_list = filter ((== 1) . a136522) a033075_list
Join[Range[9],Select[Range[70000],Union[Abs[Differences[ IntegerDigits[ #]]]] == {1}&&PalindromeQ[#]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 16 2021 *)
def ok(n): return "".join(sorted(str(n))) in "123456789" print([k for k in range(999) if ok(k)]) # Michael S. Branicky, Aug 04 2022
# alternate for generating full sequence instantly
from itertools import permutations
frags = ["123456789"[i:j] for i in range(9) for j in range(i+1, 10)]
afull = sorted(int("".join(s)) for f in frags for s in permutations(f))
print(afull[:70]) # Michael S. Branicky, Aug 04 2022
a(1) = 1 as a(0) = 0 and the two numbers that can be created from 0 are 0 and 1, since 0 cannot have 1 subtracted. 0 has already occurred so 1 must be chosen. a(20) = 28 as a(19) = 19 and the nine numbers that can be created from 19 are 8,9,10,18,19,110,28,29,210. The numbers 8,9,10,18,19 have already occurred and 28 is the smallest of the other four possibilities, so 28 is chosen. a(29) = 30 as a(28) = 20 and the six numbers that can be created from 20 are 10,11,20,21,30,31. The numbers 10,11,20,21 have already occurred and 30 is the smallest of the other two possibilities, so 30 is chosen. a(1870) = 995 as a(1869) = 1886 and of the 81 possible numbers that can be created from 1886, 995 is the smallest that has not previously occurred. This example shows that the terms can have a large drop in value if the leading digit can decrease by 1. a(1875) = 8108 as a(1874) = 999 and of the 27 possible numbers that can be created from 999, 8108 is the smallest that has not previously occurred. This example shows that the terms can have a large increase in value if any of its 9 digits are forced to increase to 10.
Nest[Block[{a = #, n = #[[-1]]}, Append[a, SelectFirst[Union@ Map[FromDigits@ DeleteCases[Flatten@ IntegerDigits[IntegerDigits[n] + #], ?(AnyTrue[#, # < 0 &] &)] &, Tuples[{-1, 0, 1}, IntegerLength[n]]], FreeQ[a, #] &]]] &, {0, 1}, 71] (* _Michael De Vlieger, Feb 27 2021 *)
t = {1, 2, 3, 4, 5, 6, 7, 8, 9}; Do[AppendTo[t, 10*t[[-1]]]; AppendTo[t, 10*t[[-1]] + 9], {9}]; t (* T. D. Noe, Oct 22 2013 *)
def A198486(): print('Numbers whose consecutive digits differ by 9') for i in range(1, 100001): b, n = True, i if n > 9: while n > 9: a = abs((n // 10) % 10 - n % 10) if a != 9: b = False n = n // 10 if b: print(i, end=', ') return
a(1) = 1 as a(0) = 0 and the only number that can be created, since 0 can only be added to, is 0 + 1 = 1. a(10) = 10 as a(9) = 9 and the two number that can be created from 9 are 8 and 10, but 8 has already occurred so 10 must be chosen. a(11) = 21 as a(10) = 10 and the two numbers that can be created from 10 are '01' = 1 and 21, but 1 has already occurred so 21 must be chosen. a(12) = 12 as (11) = 21 and the four numbers that can be created from 21 are 10, 12, 30, 32. The number 10 has already occurred and 12 is the smallest of the other three possibilities, so 12 is chosen. a(28) = 30 as a(27) = 41 and the four numbers that can be created from 41 are 30, 32, 50, 52. The number 30 has not previously occurred and is the smallest of the possibilities, so 30 is chosen. From 30 the two numbers that can be created are 21 and 41, both of which have already occurred, so the sequence terminates.
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