A064735 -id:A064735 - cp's OEIS frontend

A252629 a(n) = A064735(n) - A000040(n).

21, 10, 48, 10, 102, 100, 156, 172, 200, 200, 100, 100, 200, 388, 300, 300, 300, 400, 100, 200, 100, 100, 200, 300, 100, 912, 928, 5000, 982, 2000, 1150, 1188, 1236, 1260, 1344, 1000, 1414, 1000, 3000, 1560, 2000, 1000, 1722, 1000, 1776, 1794, 1900, 1000, 2046, 1000, 2100, 2000

Offset: 1

Zak Seidov, Dec 19 2014

nonn

Zak Seidov, Table of n, a(n) for n = 1..2000

Cf. A000040, A064735.

p = 1; s = {}; m = 100; Do[p = NextPrime[p]; idp = IntegerDigits[p]; le = Length[idp]; q = p; Label[1]; q = NextPrime[q]; par = Partition[IntegerDigits[q], le, 1]; If[MemberQ[par, idp], AppendTo[s, q - p]; Goto[2], Goto[1]]; Label[2], {m}];s(*for first m terms*)

A100844 Smallest m greater than n such that m^2 contains n^2 in its decimal representation.

Original entry on oeis.org

10, 4, 7, 7, 13, 15, 19, 43, 42, 41, 90, 110, 38, 130, 140, 35, 160, 170, 57, 190, 80, 210, 220, 227, 240, 75, 260, 223, 279, 196, 70, 219, 320, 330, 340, 285, 360, 370, 380, 390, 400, 410, 343, 136, 440, 205, 460, 470, 480, 490, 150, 510, 520, 530, 540, 305, 481

Offset: 0

Reinhard Zumkeller, Jan 14 2005

a(n) <= 10*n; a(A102576(n)) < 10*A102576(n), a(A102577(n)) = 10*A102577(n). - Reinhard Zumkeller, Jan 15 2005

			n=3: (3+1)^2 = 16, (3+2)^2 = 25 and (3+3)^2 = 36 do not contain 9 = 3^2, but 7^2 = 49 contains 9, therefore a(3) = 7.

Zak Seidov, Table of n, a(n) for n = 0..1000

Cf. A000290, A064735, A102576, A102577.

p = -1; s = {}; m = 100; Do[p = p + 1; idp = IntegerDigits[p^2]; le = Length[idp]; q = p; Label[1]; q = q + 1; par = Partition[IntegerDigits[q^2], le, 1]; If[MemberQ[par, idp], AppendTo[s, q]; Goto[2], Goto[1]]; Label[2], {m}]; s (* Zak Seidov, Dec 19 2014 *)
f[n_] := Block[{sidn = ToString[n^2], k = n + 1}, While[ StringPosition[ ToString[k^2], sidn] == {}, k++]; k]; Array[f, 60, 0] (* Robert G. Wilson v, Dec 19 2014 *)

def a(n):
    s, m = str(n*n), n+1
    while s not in str(m*m): m += 1
    return m
print([a(n) for n in range(57)]) # Michael S. Branicky, Oct 04 2021

A381606 a(n) is the smallest prime number greater than n that contains n as a substring of its digits.

Original entry on oeis.org

101, 11, 23, 13, 41, 53, 61, 17, 83, 19, 101, 113, 127, 113, 149, 151, 163, 173, 181, 191, 1201, 211, 223, 223, 241, 251, 263, 127, 281, 229, 307, 131, 1321, 233, 347, 353, 367, 137, 383, 139, 401, 241, 421, 431, 443, 457, 461, 347, 487, 149, 503, 151, 521, 353, 541

Offset: 0

Joost de Winter, Mar 01 2025

			The first prime number greater than 0 that contains "0" is 101, so a(0) = 101.
The first prime number greater than 1 that contains "1" is 11, so a(1) = 11.
The first prime number greater than 2 that contains "2" is 23, so a(2) = 23.

Joost de Winter, Table of n, a(n) for n = 0..9000
David A. Corneth, PARI program
Joost de Winter, MATLAB function

Cf. A062584, A354114, A381099, A064735.

MATLAB
```
\\ See De Winter link
```

f:= proc(n) local m,d,d1,x,y,L;
  m:= length(n);
  for d from 1 do
    L:= sort([seq(10^d * n + x, x = 1 .. 10^d-1, 2),
             seq(n+10^m*x, x=10^(d-1) .. 10^d-1),
             seq(seq(seq(10^d1*n + x + 10^(m+d1)*y, x=1 .. 10^d1-1,2),y=10^(d-d1-1) .. 10^(d-d1)-1),d1=1..d-1)]);
    for x in L do if isprime(x) then return x fi od
  od
end proc:
f(0):= 101:
map(f, [$0..100]); # Robert Israel, Mar 02 2025

a[n_] := Module[{p = NextPrime[n + 1], s = ToString[n]}, While[! StringContainsQ[ToString[p], s], p = NextPrime[p]]; p]; Array[a, 100, 0] (* Amiram Eldar, Mar 03 2025 *)

a(n) = my(p=nextprime(n+1), s=Str(n)); while (#strsplit(Str(p), s) < 2, p = nextprime(p+1)); p; \\ Michel Marcus, Mar 01 2025

PARI
```
\\ See Corneth link
```

a(n) > 2n. For large enough n, a(n) < n^5 by the strongest known version of Linnik's theorem. - Charles R Greathouse IV, Mar 01 2025

cp's OEIS Frontend

A252629 a(n) = A064735(n) - A000040(n).

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A100844 Smallest m greater than n such that m^2 contains n^2 in its decimal representation.

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A381606 a(n) is the smallest prime number greater than n that contains n as a substring of its digits.

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