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.
A383061Q[k_] := MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?OddQ} /; i >= j]; Select[Range[200], A383061Q]
def ok(n):
s = str(n)
return any(s[i] <= s[i-1] for i in range(1, len(s)) if s[i] in "13579")
print([k for k in range(200) if ok(k)]) # Michael S. Branicky, Apr 19 2025
A383062Q[k_] := FreeQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?OddQ} /; i >= j]; Select[Range[0, 100], A383062Q]
def ok(n):
s = str(n)
return all(s[i+1] > s[i] for i in range(len(s)-1) if s[i+1] in "13579")
print([k for k in range(91) if ok(k)]) # Michael S. Branicky, Apr 19 2025
A382462list[nmax_] := Module[{a, s, invQ, fu = 2}, invQ[k_] := invQ[k] = (If[#, s[k] = #]; #) & [MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i >= j]]; s[_] := False; s[1] = True; NestList[(a = fu; While[s[a] || invQ[a] || invQ[# + First[IntegerDigits[a]]], a++] & [Mod[#, 10]*10]; While[s[fu], fu++]; s[a] = True; a) &, 1, nmax-1]]; A382462list[100]
from itertools import count, islice
def cond(s):
return all(s[i] > s[i-1] for i in range(1, len(s)) if s[i] in "02468")
def agen(): # generator of terms
an, seen, s, m = 1, {1}, "1", 1
while True:
yield an
an = next(k for k in count(m) if k not in seen and cond(s[-1]+str(k)))
seen.add(an); s += str(an)
while m in seen or not cond(str(m)): m += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Apr 19 2025
A382935list[nmax_] := Module[{a, s, invQ, fu = 1}, invQ[k_] := invQ[k] = (If[#, s[k] = #]; #) & [MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?OddQ} /; i <= j]]; s[_] := False; s[0] = True; NestList[(a = fu; While[s[a] || invQ[a] || invQ[# + First[IntegerDigits[a]]], a++] & [Max[Mod[#, 10], 1]*10]; While[s[fu], fu++]; s[a] = True; a) &, 0, nmax - 1]]; A382935list[100]
from itertools import count, islice
def cond(s):
return all(s[i+1] < s[i] for i in range(len(s)-1) if s[i+1] in "13579")
def agen(): # generator of terms
an, seen, s, m = 0, {0}, "0", 1
while True:
yield an
an = next(k for k in count(m) if k not in seen and cond(s[-1]+str(k)))
seen.add(an); s += str(an)
while m in seen or not cond(str(m)): m += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Apr 14 2025
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