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.

Previous Showing 11-18 of 18 results.

A046369 Numbers with exactly 3 prime factors (counted with multiplicity), all of which are palindromes.

Original entry on oeis.org

8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 63, 66, 70, 75, 98, 99, 105, 110, 125, 147, 154, 165, 175, 231, 242, 245, 275, 343, 363, 385, 404, 524, 539, 604, 605, 606, 724, 764, 786, 847, 906, 909, 1010, 1086, 1146, 1179, 1252, 1310, 1331, 1359, 1412, 1414
Offset: 1

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Links

Crossrefs

Intersection of A033620 and A014612.
Cf. A046401.

Programs

  • Mathematica
    Select[Range[1500],PrimeOmega[#]==3&&AllTrue[FactorInteger[#][[;;,1]],PalindromeQ]&] (* Harvey P. Dale, Jul 04 2025 *)
  • Python
    from sympy import factorint
def pal(n): s = str(n); return s == s[::-1]
def ok(n):
    f = factorint(n)
    return sum(f.values())==3 and all(pal(p) for p in f)
print([k for k in range(1415) if ok(k)]) # Michael S. Branicky, Jul 04 2025

Extensions

Offset changed by Andrew Howroyd, Aug 14 2024
Name clarified by Sean A. Irvine, Jul 04 2025

A046370 Numbers with exactly 4 palindromic prime factors (counted with multiplicity).

Original entry on oeis.org

16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 126, 132, 135, 140, 150, 189, 196, 198, 210, 220, 225, 250, 294, 297, 308, 315, 330, 350, 375, 441, 462, 484, 490, 495, 525, 550, 625, 686, 693, 726, 735, 770, 808, 825, 875, 1029, 1048, 1078, 1089, 1155, 1208
Offset: 1

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Links

Crossrefs

Intersection of A033620 and A014613.
Cf. A046402.

Extensions

Offset changed by Andrew Howroyd, Aug 14 2024

A046371 Numbers with exactly 5 palindromic prime factors (counted with multiplicity).

Original entry on oeis.org

32, 48, 72, 80, 108, 112, 120, 162, 168, 176, 180, 200, 243, 252, 264, 270, 280, 300, 378, 392, 396, 405, 420, 440, 450, 500, 567, 588, 594, 616, 630, 660, 675, 700, 750, 882, 891, 924, 945, 968, 980, 990, 1050, 1100, 1125, 1250, 1323, 1372, 1386, 1452
Offset: 1

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Links

Crossrefs

Intersection of A033620 and A014614.
Cf. A046403.

Extensions

Offset changed by Andrew Howroyd, Aug 14 2024

A046374 Odd numbers with exactly 4 palindromic prime factors (counted with multiplicity).

Original entry on oeis.org

81, 135, 189, 225, 297, 315, 375, 441, 495, 525, 625, 693, 735, 825, 875, 1029, 1089, 1155, 1225, 1375, 1617, 1715, 1815, 1925, 2401, 2541, 2695, 2727, 3025, 3537, 3773, 3993, 4077, 4235, 4545, 4887, 5157, 5895, 5929, 6363, 6655, 6795, 7575, 8145, 8253
Offset: 1

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Links

Crossrefs

Intersection of A033620 and A046317.
Cf. A046406.

Extensions

Offset changed by Andrew Howroyd, Aug 14 2024

A342572 Positive numbers all of whose prime factors are binary palindromes.

Original entry on oeis.org

1, 3, 5, 7, 9, 15, 17, 21, 25, 27, 31, 35, 45, 49, 51, 63, 73, 75, 81, 85, 93, 105, 107, 119, 125, 127, 135, 147, 153, 155, 175, 189, 217, 219, 225, 243, 245, 255, 257, 279, 289, 313, 315, 321, 343, 357, 365, 375, 381, 405, 425, 441, 443, 459, 465, 511, 525, 527
Offset: 1

Views

Author

Amiram Eldar, Mar 27 2021

Keywords

Examples

			15 is a term since the binary representation of its prime factors, 3 and 5, are both palindromes: 11 and 101.
1 is a term because it has no prime factors, and "the empty set has every property". - _N. J. A. Sloane_, Jan 16 2022

Links

Crossrefs

The binary version of A033620.
Subsequences: A016041, A329419.
Cf. A006995.

Programs

  • Mathematica
    seq[max_] := Module[{ps = Select[Range[max], PalindromeQ @ IntegerDigits[#, 2] && PrimeQ[#] &], s = {1}, s1, s2}, Do[p = ps[[k]]; emax = Floor@Log[p, max]; s1 = Join[{1}, p^Range[emax]]; s2 = Select[Union[Flatten[Outer[Times, s, s1]]], # <= max &]; s = Union[s, s2], {k, 1, Length[ps]}]; s]; seq[1000]
Join[{1},Module[{bps=Select[Prime[Range[200]],IntegerDigits[#,2] == Reverse[ IntegerDigits[ #,2]]&]},Select[ Range[Max[ bps]],SubsetQ[ bps,FactorInteger[#][[All,1]]]&]]] (* Harvey P. Dale, Jan 16 2022 *)
  • Python
    from sympy import factorint
def ispal(s): return s == s[::-1]
def ok(n): return n > 0 and all(ispal(bin(f)[2:]) for f in factorint(n))
print([k for k in range(528) if ok(k)]) # Michael S. Branicky, Jan 17 2022

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A016041} p/(p-1) = 2.52136...

Extensions

"Positive" added to definition by N. J. A. Sloane, Jan 16 2022

A376858 Fixed points of A071786.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 101, 105, 108, 110, 112, 120, 121, 125, 126, 128, 131, 132, 135, 140
Offset: 1

Views

Author

Paolo Xausa, Oct 07 2024

Keywords

Comments

First differs from A033620 at n = 139. In the present sequence a(139) = 403 = 13 * 31: 13 and 31 are the reversals of each other but neither is a palindrome, so 403 is not in A033620.

Links

Crossrefs

Cf. A071786. Supersequence of A033620.

Programs

  • Mathematica
    A376858Q[k_] := k == Times @@ (IntegerReverse[#1]^#2 & @@@ FactorInteger[k]);
Select[Range[200], A376858Q]

A334140 Numbers that can be written as a product of distinct palindromes.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 54, 55, 56, 60, 63, 64, 66, 70, 72, 77, 80, 84, 88, 90, 96, 99, 101, 105, 108, 110, 111, 112, 120, 121, 126, 131, 132, 135, 140
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 15 2020

Keywords

Links

Crossrefs

Cf. A002113, A033620, A084034, A115683, A140332, A334131.

Programs

  • Mathematica
    ok[n_, w_: {}] := n <= 1 || AnyTrue[ Divisors@ n, ! MemberQ[w, #] && PalindromeQ[#] && ok[n/#, Append[w, #]] &]; Select[Range[0, 140], ok] (* Giovanni Resta, Apr 15 2020 *)

A372629 Prime numbers whose sum of digits is a palindrome.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 41, 43, 47, 53, 61, 71, 83, 101, 103, 107, 113, 131, 137, 151, 173, 191, 211, 223, 227, 233, 241, 251, 263, 281, 311, 313, 317, 331, 353, 401, 421, 431, 443, 461, 499, 503, 521, 601, 641, 701, 769, 787, 821, 859, 877, 911, 967, 1013, 1019, 1021, 1031, 1033, 1051
Offset: 1

Views

Author

James S. DeArmon, May 07 2024

Keywords

Examples

			2411 is a term (prime, and digits sum to 8, a palindrome);
9931 is a term (prime, and digits sum to 22, a palindrome);
10099997 is a term (prime, and digits sum to 44).

Links

Crossrefs

Cf. A002385, A007500, A033620.

Programs

  • Mathematica
    Select[Prime[Range[200]], PalindromeQ[DigitSum[#]] &] (* Paolo Xausa, Feb 27 2025 *)
  • Python
    import sympy
def sum_of_digits(n):
    return sum(int(digit) for digit in str(n))
def is_palindrome(n):
    return str(n) == str(n)[::-1]
# Find prime numbers between 1 and 10000 whose sum of digits is a palindrome
prime_palindrome_numbers = []
for num in range(1,10000):
    if sympy.isprime(num):
        digit_sum = sum_of_digits(num)
        if is_palindrome(digit_sum):
            prime_palindrome_numbers.append(num)
print(prime_palindrome_numbers)
(Common Lisp) ; See Links section.
Previous Showing 11-18 of 18 results.

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

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