cp's OEIS Frontend

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.

Showing 1-7 of 7 results.

A061246 Prime having only {0, 1, 4, 9} as digits.

Original entry on oeis.org

11, 19, 41, 101, 109, 149, 191, 199, 401, 409, 419, 449, 491, 499, 911, 919, 941, 991, 1009, 1019, 1049, 1091, 1109, 1409, 1499, 1901, 1949, 1999, 4001, 4019, 4049, 4091, 4099, 4111, 4409, 4441, 4909, 4919, 4999, 9001, 9011, 9041, 9049, 9091, 9109, 9199
Offset: 1

Views

Author

Amarnath Murthy, Apr 23 2001

Keywords

Examples

			a(10) = 419, 419 is a prime and 1, 4 and 9 are squares.

Links

Crossrefs

Cf. A066591.

Programs

  • Mathematica
    Select[FromDigits/@Tuples[{0,1,4,9},4],PrimeQ] (* Harvey P. Dale, Sep 22 2019 *)
  • Python
    from itertools import product
from sympy import isprime
A061246_list = [int(i+''.join(j)+k) for l in range(10) for i in '149' for j in product('0149',repeat=l) for k in '19' if isprime(int(i+''.join(j)+k))] # Chai Wah Wu, Jan 19 2019

Extensions

Corrected and extended by Jason Earls, May 17 2005
Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

A066592 Primes which can be expressed as concatenation of cubes.

Original entry on oeis.org

11, 101, 127, 181, 271, 641, 811, 827, 881, 1181, 1801, 1811, 2161, 2711, 6427, 6481, 8011, 8081, 8101, 8111, 8641, 10111, 10181, 10271, 10343, 10729, 11027, 11251, 11801, 11827, 12161, 12197, 12511, 12527, 12781
Offset: 1

Views

Author

Amarnath Murthy, Dec 21 2001

Keywords

Examples

			2161 is a term as it is a concatenation of 216 and 1 both of which are cubes. 8081 is a term as it is a concatenation of 8, 0, 8 and 1 all of which are cubes.

Crossrefs

Cf. A066591.

Extensions

Corrected and extended by Christopher Lund (clund(AT)san.rr.com), Apr 14 2002

A066593 Primes which can be expressed as concatenation of powers of 2 and 0's.

Original entry on oeis.org

2, 11, 41, 101, 181, 211, 241, 281, 401, 421, 641, 811, 821, 881, 1021, 1181, 1201, 1321, 1481, 1601, 1621, 1801, 1811, 2011, 2081, 2111, 2141, 2161, 2221, 2281, 2411, 2441, 2801, 3221, 4001, 4021, 4111, 4201, 4211, 4241, 4421, 4441, 4481
Offset: 1

Views

Author

Amarnath Murthy, Dec 21 2001

Keywords

Examples

			1321 is a term as it is a concatenation of 1, 32 and 1 which are powers of 2.

Crossrefs

Cf. A066591, A066592.

Extensions

Corrected and extended by Christopher Lund (clund(AT)san.rr.com), Apr 14 2002

A173580 Primes where each digit is 0, 1, 2, 4, or 8.

Original entry on oeis.org

2, 11, 41, 101, 181, 211, 241, 281, 401, 421, 811, 821, 881, 1021, 1181, 1201, 1481, 1801, 1811, 2011, 2081, 2111, 2141, 2221, 2281, 2411, 2441, 2801, 4001, 4021, 4111, 4201, 4211, 4241, 4421, 4441, 4481, 4801, 8011, 8081, 8101, 8111, 8221, 8821, 10111
Offset: 1

Views

Author

Michel Lagneau, Feb 22 2010

Keywords

Links

Crossrefs

See A066593.
Cf. A066591, A066592.

Programs

  • Maple
    with(numtheory): for n from 2 to 10000 do: l:=evalf(floor(ilog10(n))+1): n0:=n:indic:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10): n0:=v : if u=3 or u= 5 or u= 6 or u=7 or u=9 then indic :=1 :else fi :od :if indic = 0 and type(n,prime) = true then print(n):else fi:od:
  • Mathematica
    Join[{2}, Select[Map[FromDigits, Tuples[{0, 1, 2, 4, 8}, 3]]*10 + 1, PrimeQ]] (* Paolo Xausa, Jun 12 2025 *)
  • Python
    from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    yield 2
    yield from (t for digits in count(2) for f in "1248" for mid in product("01248", repeat=digits-2) if isprime(t:=int(f + "".join(mid) + "1")))
print(list(islice(agen(), 45))) # Michael S. Branicky, Jun 11 2025

A068493 Primes which are concatenations of positive squares.

Original entry on oeis.org

11, 19, 41, 149, 181, 191, 199, 251, 419, 449, 491, 499, 641, 811, 911, 919, 941, 991, 1009, 1181, 1259, 1289, 1361, 1481, 1499, 1619, 1699, 1811, 1949, 1999, 2251, 2549, 2591, 3691, 4001, 4111, 4259, 4289, 4441, 4481, 4649, 4729, 4919, 4999, 6449, 6481, 6491
Offset: 1

Views

Author

Joseph L. Pe, Mar 11 2002

Keywords

Examples

			149 is a term of the sequence since it is the concatenation of squares 1, 4, 9.
251 is a term of the sequence since it is the concatenation of squares 25, 1. - _Sean A. Irvine_, Feb 19 2024

Links

Crossrefs

Cf. A000290, subsequence of A066591.

Programs

  • Python
    from sympy import primerange
from itertools import count, islice
def iscat(w, A):
    return False if len(w) < 2 else any(w[:i] in A and (w[i:] in A or iscat(w[i:], A)) for i in range(1, len(w)))
def agen():
    S = set()
    for d in count(2):
        S |= {str(i*i) for i in range(10**(d-2), 10**(d-1))}
        for p in primerange(10**(d-1), 10**d):
            if iscat(str(p), S):
                yield p
print(list(islice(agen(), 50))) # Michael S. Branicky, Feb 20 2024

Extensions

Corrected and extended by Sascha Kurz, Mar 26 2002
Data corrected by Sean A. Irvine, Feb 19 2024

A331346 Primes using all the square digits {0, 1, 4, 9} and no others.

Original entry on oeis.org

1049, 1409, 4019, 4091, 9041, 10499, 10949, 14009, 49019, 49109, 90149, 90401, 94109, 99041, 99401, 100049, 101149, 101419, 101449, 104009, 104119, 104149, 104491, 104911, 104999, 109049, 109141, 109441, 110419, 110491, 111049, 111409, 114901, 140009, 140191, 140419
Offset: 1

Views

Author

K. D. Bajpai, Jan 14 2020

Keywords

Comments

Subsequence of A061246.

Examples

			a(1) = 1049 is prime containing all the square digits (0, 1, 4, 9) and no others.
a(2) = 1409 is prime containing all the square digits (0, 1, 4, 9) and no others.

Links

Crossrefs

Cf. A000040, A061246, A066591, A323387.

Programs

  • Magma
    [p:p in PrimesUpTo(150000)|Set(Intseq(p)) eq {0,1,4,9}]; // Marius A. Burtea, Jan 14 2020
  • Maple
    f:= proc(n) local L,x;
  L:= convert(n,base,4);
  if convert(L,set) <> {0,1,2,3} then return NULL fi;
  L:= subs(2=4,3=9,L);
  x:= add(L[i]*10^(i-1),i=1..nops(L));
  if isprime(x) then x else NULL fi
end proc:
map(f, [$4^3..4^6]); # Robert Israel, Jan 16 2020
  • Mathematica
    Select[FromDigits /@ Tuples[{0, 1, 4, 9}, 6], PrimeQ[#] && Union[IntegerDigits[#]] == {0, 1, 4, 9} &]

A066594 Primes which can be expressed as concatenation of powers of 3 and 0's.

Original entry on oeis.org

3, 11, 13, 19, 31, 101, 103, 109, 113, 127, 131, 139, 181, 191, 193, 199, 271, 311, 313, 331, 811, 911, 919, 991, 1009, 1013, 1019, 1031, 1033, 1039, 1091, 1093, 1103, 1109, 1181, 1193, 1279, 1301, 1303, 1319, 1327, 1381, 1399, 1811, 1901, 1913, 1931
Offset: 1

Views

Author

Amarnath Murthy, Dec 21 2001

Keywords

Examples

			271 is a term as it is a concatenation of 27 and 1 which are powers of 3.

Crossrefs

Cf. A066591, A066592, A066593.

Extensions

Corrected and extended by Christopher Lund (clund(AT)san.rr.com), Apr 14 2002
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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