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A356498 Primes p such that 100*p + 11 is also prime.

2, 3, 23, 41, 83, 101, 107, 113, 137, 179, 233, 239, 251, 281, 293, 353, 359, 401, 419, 479, 503, 557, 563, 569, 587, 683, 701, 743, 809, 839, 857, 863, 941, 953, 977, 1049, 1091, 1103, 1193, 1217, 1277, 1283, 1361, 1367, 1427, 1487, 1499, 1523, 1607, 1619, 1847, 1871, 1877, 1889, 1907, 1949, 1973

Offset: 1

Daniel Blam, Aug 09 2022

nonn

100*p + 11 has the effect of appending 11 to p.

Primes of the form 3*k + 1 are never in this sequence, as 100*(3*k + 1) + 11 can be simplified to 3*(100*k + 37).

			2 is a term, as 100*2 + 11 is 211, which are both prime.
101 is a term, as 100*101 + 11 is 10111 which are both prime.

Cf. A000040, A002476 (primes of the form 3*k+1).

Similar to A023237.

from sympy import isprime
print([k for k in range(2000) if isprime(100*k+11) and isprime(k)])

A356417 Numbers whose reversal is a square.

Original entry on oeis.org

0, 1, 4, 9, 10, 18, 40, 46, 52, 61, 63, 90, 94, 100, 121, 144, 148, 163, 169, 180, 400, 423, 441, 460, 484, 487, 520, 522, 526, 610, 630, 652, 675, 676, 691, 900, 925, 927, 940, 961, 982, 1000, 1042, 1062, 1089, 1210, 1251, 1273, 1297, 1405, 1426, 1440, 1480

Offset: 1

Daniel Blam, Aug 06 2022

Every power of 10 is a term in the sequence.
If k is in the sequence then so is 10*k. - David A. Corneth, Aug 06 2022
If all multiples of 10 were omitted, A074896 would result. - Jon E. Schoenfield, Aug 06 2022

			0 is a term, 0 -> 0 (0^2).
10 is a term, 10 -> 01 (leading zero is dropped) (1^2).
691 is a term, 691 -> 196 (14^2).
1800 is a term, 1800 -> 0081 (leading zeros are dropped) (9^2).

Cf. A002942, A004086, A074896.

Select[Range[0, 1500], IntegerQ[Sqrt[IntegerReverse[#]]] &] (* Amiram Eldar, Aug 06 2022 *)

isok(k) = issquare(fromdigits(Vecrev(digits(k)))); \\ Michel Marcus, Aug 06 2022

from sympy import integer_nthroot
def ok(n):
    return integer_nthroot(int(str(n)[::-1]), 2)[1]
print([k for k in range(1500) if ok(k)])

from math import isqrt
from itertools import count, islice
def A356417_gen(): # generator of terms
    yield 0
    for l in count(1):
        nlist = []
        for m in range(1,isqrt(10**l)+1):
            if m%10:
                s = str(m**2)
                nlist.append(int(s[::-1])*10**(l-len(s)))
        yield from sorted(nlist)
A356417_list = list(islice(A356417_gen(),100)) # Chai Wah Wu, Aug 07 2022

A349460 Squares composed of digits {0,2,4}.

Original entry on oeis.org

0, 4, 400, 40000, 2244004, 4000000, 42224004, 224400400, 400000000, 424442404, 4222400400, 22200404004, 22440040000, 40000000000, 42444240400, 422240040000, 2220040400400, 2244004000000, 4000000000000, 4024044024004, 4244424040000, 40244204444224, 42224004000000

Offset: 1

Daniel Blam, Nov 18 2021

From Marius A. Burtea, Nov 18 2021: (Start)
The sequence is infinite because if m > 0 is a term, then 100*m is also a term.
Also, the squares of the numbers 20602, 2006002, 200060002, ..., (2*10^(2*k) + 6*10^k + 2), k >= 2, are 424442404, 4024044024004, 40024004400240004, 400024000440002400004, ... and have only the digits 0, 2 and 4 and are not divisible by 100. (End)

Subsequence of A000290 and A030098.

[n : n in [s*s:s in [1..1500000]]|Set(Intseq(n)) subset {0,2,4}]; // Marius A. Burtea, Nov 18 2021

Select[Range[0, 10^7, 2]^2, AllTrue[IntegerDigits[#], MemberQ[{0, 2, 4}, #1] &] &] (* Amiram Eldar, Nov 18 2021 *)

from itertools import islice, count
def A349460(): return filter(lambda n: set(str(n)) <= {'0','2','4'},(n*n for n in count(0)))
A349460_list = list(islice(A349460(),20)) # Chai Wah Wu, Nov 19 2021

A342975 Cubes composed of digits {0, 1, 3}.

Original entry on oeis.org

0, 1, 1000, 1331, 1000000, 1030301, 1331000, 1000000000, 1003003001, 1030301000, 1331000000, 1000000000000, 1000300030001, 1003003001000, 1030301000000, 1331000000000, 1000000000000000, 1000030000300001, 1000300030001000, 1003003001000000, 1030301000000000, 1331000000000000

Offset: 1

Daniel Blam, Nov 19 2021

This sequence is infinite, because if m > 0 is a term, 1000*m will also be a term.

Subsequence of A000578 and A043681.

Select[Range[0, 110000]^3, AllTrue[IntegerDigits[#], MemberQ[{0, 1, 3}, #1] &] &] (* Amiram Eldar, Nov 19 2021 *)

from itertools import islice, count
def A342975(): return filter(lambda n: set(str(n)) <= {'0','1','3'},(n**3 for n in count(0)))
A342975_list = list(islice(A342975(),20)) # Chai Wah Wu, Nov 19 2021

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User: Daniel Blam

A356498 Primes p such that 100*p + 11 is also prime.

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A356417 Numbers whose reversal is a square.

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PARI

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A349460 Squares composed of digits {0,2,4}.

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Magma

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Python

A342975 Cubes composed of digits {0, 1, 3}.

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Mathematica

Python