A048380 -id:A048380 - cp's OEIS frontend

A222210 In the number n, replace all (decimal) digits '0' with '1' and vice versa.

1, 0, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 2, 3, 4, 5, 6, 7, 8, 9, 21, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 30, 32, 33, 34, 35, 36, 37, 38, 39, 41, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 60, 62, 63, 64, 65, 66, 67, 68, 69, 71, 70, 72, 73, 74, 75

Offset: 0

M. F. Hasler, Feb 12 2013

The map which is applied to primes in A171013 and A175791.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A171013, A175791; A048380.

a[n_] := IntegerDigits[n] /. {0 -> 1, 1 -> 0} // FromDigits; Table[a[n], {n, 0, 75}] (* Jean-François Alcover, Jun 11 2013 *)

A222210(n,d=[1,0,2,3,4,5,6,7,8,9])=sum(i=1,#n=digits(n),d[n[i]+1]*10^(#n-i),!n) \\ N.B.: PARI's digits() function returns [] for 0.

A329147 Replace in n each nonzero digit d with prime(d).

Original entry on oeis.org

0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 20, 22, 23, 25, 27, 211, 213, 217, 219, 223, 30, 32, 33, 35, 37, 311, 313, 317, 319, 323, 50, 52, 53, 55, 57, 511, 513, 517, 519, 523, 70, 72, 73, 75, 77, 711, 713, 717, 719, 723, 110, 112, 113, 115, 117, 1111, 1113, 1117, 1119, 1123

Offset: 0

Bernard Schott, Nov 06 2019

Some properties:
No term has a digit 4, 6 or 8.
No term begins with 9, 10, 12, 15, 29, 39, 59, 79.
If a is regarded as a function a: n --> a(n) from N to N, then
1) a is neither increasing: a(9) > a(10) nor decreasing: a(3) < a(4),
2) a is not injective: a(92) = a(122) = 233,
3) a is not surjective: 4 and 15 are not terms. The integers that are not in this sequence are in A329149 and the integers that are obtained are in A329150, with increasing order.
Some primes remain primes: 2, 3, 5, 7, 19, 59, ...
Some primes become composites: 11, 13, 17, 23, 29, 31, ...
Some composites remain composites: 10, 14, 16, 18, 20, 21, 22,...
Some composites become primes: 4, 6, 8, 9, 12, 15, 24, 25, 26,...
When n > 4 ends respectively with 0, 1 or 3 then a(n) that ends with 0, 2, 5 is composite.
The sequence 9, 99, 999, ..., respectively 12, 1212, 121212, ... generates the same numbers 23, 2323, 232323, ... Analogously, 9, 92, 922, 922, ... and 12, 122, 1222, ... generate the same sequence 23, 233, 2333, 23333, .... For the numbers 91,9191,919191, ... the terms of the sequence are 232, 232232, 232232232, ... so palindromes. - Marius A. Burtea, Nov 07 2019
The numbers 113, 14113, 1441113, 144411113, ... determine the terms 225 = 15^2, 27225 = 165^2, 2772225 = 1665^2, ... (in A191486). The numbers 14, 14000, 14000000, ... determine the terms 27 = 3^3, 27000 = 30^3, 27000000 = 300^3, .... - Marius A. Burtea, Nov 12 2019

			As a(2) = prime(2) = 3, a(5) = prime(5) = 11 and a(8) = prime(8) = 19, a(258)= 31119.
As a(3) = prime(3) = 5, a(0) = 0 and a(7) = prime(7) = 17, hence a(307) = 5017.

Metin Sariyar, Table of n, a(n) for n = 0..10000

Cf. A000040, A329149, A329150.

Similar to A048380, A048385 and A322131.

v:=[0,2,3,5,7,11,13,17,19,23]; [0] cat [StringToInteger(&cat[IntegerToString(k): k in Reverse([v[m+1]: m in Intseq(n)])]): n in [1..60]]; // Marius A. Burtea, Nov 07 2019

a:= n-> (l-> parse(cat(seq(`if`(l[-i]=0, 0, ithprime(l[-i])),
             i=1..nops(l)))))(convert(n, base, 10)):
seq(a(n), n=0..80);  # Alois P. Heinz, Nov 07 2019

p[n_] := If[n > 0, Prime[n], 0]; a[n_] := FromDigits[Flatten @ IntegerDigits @ (p /@ IntegerDigits[n])]; Array[a, 60, 0] (* Amiram Eldar, Nov 06 2019 *)

a(n) = if (n, fromdigits(concat(apply(d -> if (d, digits(prime(d)), [0]), digits(n)))), 0) \\ Rémy Sigrist, Nov 07 2019

def A329147(n): return int("".join(map(str, ([0, 2, 3, 5, 7, 11, 13, 17, 19, 23][int(i)] for i in str(n)))))
print([A329147(n) for n in range(60)]) # Michael S. Branicky, Apr 10 2023

A048381 Numbers k such that replacing each nonzero digit d with the d-th prime (replacing each 0 digit with a 1) yields a prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 19, 20, 24, 25, 26, 27, 32, 39, 40, 42, 48, 52, 57, 59, 60, 64, 68, 72, 79, 80, 82, 84, 86, 92, 95, 100, 105, 106, 112, 114, 116, 122, 125, 130, 134, 140, 144, 145, 146, 148, 150, 152, 160, 164, 166, 167, 168, 169, 176

Offset: 1

Patrick De Geest, Mar 15 1999

			176 = (1)(7)(6) -> (2)(17)(13) = 21713, which is a prime, so 176 is in the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A048380, A048382.

filter := proc(n) local L;
  L:= convert(n,base,10);
  L:= subs([0=1,seq(i=ithprime(i),i=1..9)],L);
  L:= map(t -> op(convert(t,base,10)), L);
  isprime(add(L[i]*10^(i-1),i=1..nops(L)))
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 16 2018

Offset corrected by Robert Israel, Oct 16 2018

A048383 Numbers k such that replacing each nonzero digit d with the d-th prime (replacing each 0 digit with a 1) yields a square.

Original entry on oeis.org

0, 13, 113, 2410, 4113, 6113, 8210, 14113, 23410, 28113, 33113, 34010, 35113, 51113, 62113, 71113, 76610, 81410, 93113, 101310, 117010, 123113, 242210, 253113, 279710, 298113, 300113, 351010, 513410, 529113, 544113, 616113, 634113

Offset: 1

Patrick De Geest, Mar 15 1999

			28113 = (2)(8)(1)(1)(3) -> (3)(19)(2)(2)(5) = 319225 = 565^2.

Cf. A000290, A048380, A048384.

Select[Range[0,650000],IntegerQ[Sqrt[FromDigits[Flatten[IntegerDigits/@ (If[#==0,1,Prime[#]]&/@IntegerDigits[#])]]]]&]  (* Harvey P. Dale, Mar 27 2011 *)

Definition edited and offset corrected by M. F. Hasler, Oct 11 2019

A048384 Squares resulting from procedure described in A048383.

Original entry on oeis.org

1, 25, 225, 3721, 7225, 13225, 19321, 27225, 35721, 319225, 55225, 57121, 511225, 112225, 133225, 172225, 17131321, 192721, 235225, 212521, 2217121, 235225, 373321, 3115225, 317231721, 32319225, 511225, 5112121, 1125721, 11323225

Offset: 1

Patrick De Geest, Mar 15 1999

nonn

Cf. A048380, A048383.

A048382 Primes resulting from procedure described in A048381.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 23, 211, 223, 31, 37, 311, 313, 317, 53, 523, 71, 73, 719, 113, 1117, 1123, 131, 137, 1319, 173, 1723, 191, 193, 197, 1913, 233, 2311, 211, 2111, 2113, 223, 227, 2213, 233, 2311, 251, 257, 271, 277, 2711, 2713, 2719, 2111

Offset: 1

Patrick De Geest, Mar 15 1999

nonn

Primes in A048380 in order of their occurrence. - Andrew Howroyd, Aug 15 2024

Cf. A048380, A048381.

a(n) = A048380(A048381(n)). - Andrew Howroyd, Aug 15 2024

Offset corrected by Andrew Howroyd, Aug 15 2024

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A222210 In the number n, replace all (decimal) digits '0' with '1' and vice versa.

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A329147 Replace in n each nonzero digit d with prime(d).

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A048381 Numbers k such that replacing each nonzero digit d with the d-th prime (replacing each 0 digit with a 1) yields a prime.

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A048383 Numbers k such that replacing each nonzero digit d with the d-th prime (replacing each 0 digit with a 1) yields a square.

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A048384 Squares resulting from procedure described in A048383.

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A048382 Primes resulting from procedure described in A048381.

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