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.
0 first occurs in 101. 14 first occurs as a substring in 149.
import Data.List (isInfixOf) a062584 n = head [p | p <- a000040_list, show n `isInfixOf` show p] -- Reinhard Zumkeller, Dec 29 2011
Do[k = 1; While[ StringPosition[ ToString[Prime[k]], ToString[n]] == {}, k++ ]; Print[ Prime[k]], {n, 0, 62} ]
(* Second program *)
Function[s, Table[FromDigits@ FirstCase[s, w_ /; SequenceCount[w, IntegerDigits@ n] > 0], {n, 0, 56}]]@ IntegerDigits@ Prime@ Range[10^4] (* Michael De Vlieger, Jun 24 2017 *)
With[{prs=Prime[Range[300]]},Table[SelectFirst[prs,SequenceCount[ IntegerDigits[#], IntegerDigits[ n]]>0&],{n,0,60}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 06 2018 *)
build(root, prefixLen, suffixLen)=my(v=List(),t); for(i=10^(prefixLen-1)\1,10^prefixLen-1, t=eval(Str(i,root))*10^suffixLen; for(n=t,t+10^suffixLen-1, listput(v,n))); Vec(v) buildLen(n,d)=my(v=[]); for(i=0,d, v=concat(v,build(n,i,d-i))); Set(v) a(n)=if(n==0, return(101)); my(d,v); while(1, v=buildLen(n,d); for(i=1,#v, if(isprime(v[i]), return(v[i]))); d++) \\ Charles R Greathouse IV, Jun 23 2017
first(n) = my(res = vector(n), todo = n, g); forprime(p = 2, , d = digits(p); for(i=1,#d, if(d[i]!=0, g = d[i]; if(res[g]==0, res[g]=p; todo--); for(j=1,#d-i, g=10*g+d[i+j]; if(g>n,next(2)); if(res[g]==0, res[g]=p; todo--)))); if(todo==0,return(concat([101],res)))) \\ David A. Corneth, Jun 23 2017
from sympy import nextprime
def a(n):
p, s = 2, str(n)
while s not in str(p): p = nextprime(p)
return p
print([a(n) for n in range(57)]) # Michael S. Branicky, Dec 02 2021
import Data.List (isPrefixOf, find); import Data.Maybe (fromJust)
a018800 n = read $ fromJust $
find (show n `isPrefixOf`) $ map show a000040_list :: Int
-- Reinhard Zumkeller, Jul 01 2015
f:= proc(n) local x0, d,r,y;
if isprime(n) then return(n) fi;
for d from 1 do
x0:= n*10^d;
for r from 1 to 10^d-1 by 2 do
if isprime(x0+r) then
return(x0+r)
fi
od
od
end proc:
seq(f(n),n=1..100); # Robert Israel, Dec 23 2014
Table[Function[d, FromDigits@ SelectFirst[ IntegerDigits@ Prime@ Range[10^4], Length@ # >= Length@ d && Take[#, Length@ d] == d &]][ IntegerDigits@ n], {n, 59}] (* Michael De Vlieger, May 24 2016, Version 10 *)
a(n{,base=10}) = for (l=0, oo, forprime (p=n*base^l, (n+1)*base^l-1, return (p))) \\ Rémy Sigrist, Jun 11 2017
from sympy import isprime
def a(n):
if isprime(n): return n
pow10 = 10
while True:
t, maxt = n * pow10 + 1, (n+1) * pow10
while t < maxt:
if isprime(t): return t
t += 2
pow10 *= 10
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Nov 02 2021
Smallest square formed from 20 is 2025, by placing 25 on the right side. Smallest square formed from 33 is 3136, by inserting a 1 between 3's and placing a 6.
A068165 := proc(n) local b,pdigs,plen,dmas,dmasdigs,i,j; for b from 1 do pdigs := convert(b^2,base,10) ; plen := nops(pdigs) ; for dmas from 2^plen-1 to 0 by -1 do dmasdigs := convert(dmas,base,2) ; pdel := [] ; for i from 1 to nops(dmasdigs) do if op(i,dmasdigs) = 1 then pdel := [op(pdel),op(i,pdigs)] ; end if; end do: if n = add(op(j,pdel)*10^(j-1),j=1..nops(pdel)) then return b^2; end if; end do: end do: end proc: seq(A068165(n),n=1..133) ; # R. J. Mathar, Nov 14 2014
from math import isqrt
from itertools import count
def dmo(n, t):
if t < n: return False
while n and t:
if n%10 == t%10:
n //= 10
t //= 10
return n == 0
def a(n):
return next(t for t in (i*i for i in count(isqrt(n))) if dmo(n, t))
print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Jan 21 2023
IsSubList:= proc(T, S)
local i;
if T = [] then return true fi;
if S = [] then return false fi;
i:= ListTools:-Search(T[1],S);
if i = 0 then false else procname(T[2..-1],S[i+1..-1]) fi
end proc:
f:= proc(n) local T,S,k,v;
T:= convert(n,base,10);
for k from 1 do
v:= combinat:-fibonacci(k);
S:= convert(v,base,10);
if IsSubList(T,S) then return v fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Mar 10 2020
a[n_] := Block[{p = RegularExpression[ StringJoin @@ Riffle[ ToString /@ IntegerDigits[ n], ".*"]], f, k=2}, While[! StringContainsQ[ ToString[f = Fibonacci[ k++]], p]]; f]; Array[a, 42] (* Giovanni Resta, Mar 10 2020 *)
def dmo(n, t):
if t < n: return False
while n and t:
if n%10 == t%10:
n //= 10
t //= 10
return n == 0
def fibo(f=1, g=2):
while True: yield f; f, g = g, f+g
def a(n):
return next(f for f in fibo() if dmo(n, f))
print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Jan 21 2023
from math import isqrt
from itertools import count
def dmo(n, t):
if t < n: return False
while n and t:
if n%10 == t%10:
n //= 10
t //= 10
return n == 0
def a(n):
return next(t for t in (i*(i+1)//2 for i in count(isqrt(2*n))) if dmo(n, t))
print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Jan 21 2023
read("transforms)"):
nleadzero := proc(n,dgs)
local ndgs ;
if n = 0 then
ndgs := 0 ;
else
ndgs := ilog10(n)+1 ;
end if;
[op(convert(n,base,10)),seq(0,i=1..dgs-ndgs)]
end proc:
digcatL2 := proc(L1,L2)
digcatL([op(L1),op(L2)]) ;
end proc:
A089754 := proc(n)
local prep,a,dgs ;
if isprime(n) then
n;
elif modp(n,2) = 0 or modp(n,5) = 0 then
ndgs := convert(n,base,10) ;
for dgs from 1 do
for prep from 0 to 10^dgs-1 do
a := digcatL2(ListTools[Reverse](ndgs),ListTools[Reverse](nleadzero(prep,dgs))) ;
if isprime(a) then
return a;
end if;
end do:
end do:
else
for prep from 1 do
a := digcat2(prep,n) ;
if isprime(a) then
return a;
end if;
end do:
end if;
end proc: # R. J. Mathar, Sep 18 2015
a246398 n = a246398_list !! n
a246398_list = f 0 $ map show a000040_list where
f x pss = (length ps - length xs) :
f (x + 1) (dropWhile (== xs) pss)
where ps = head [qs | qs <- pss, isin xs qs]; xs = show x
isin [] _ = True
isin _ [] = False
isin (u:us) vs = not (null ws) && isin us ws
where ws = dropWhile (/= u) vs
a(11) = 101, because 101 is the least prime p > 11 in which the digits of 11 appear as an ordered but non-necessarily contiguous subsequence.
from sympy import sieve
def osub(n, t): # n > 0 is an ordered_subsequence of t
if t < n: return False
while n and t:
if n%10 == t%10:
n //= 10
t //= 10
return n == 0
def a(n): return next(p for p in sieve if p > n and osub(n, p)) if n else 101
print([a(n) for n in range(55)]) # Michael S. Branicky, Jul 01 2025
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