A002276 -id:A002276 - cp's OEIS frontend

A176894 Increase each digit in the binary representation of n by 2.

2, 3, 32, 33, 322, 323, 332, 333, 3222, 3223, 3232, 3233, 3322, 3323, 3332, 3333, 32222, 32223, 32232, 32233, 32322, 32323, 32332, 32333, 33222, 33223, 33232, 33233, 33322, 33323, 33332, 33333, 322222, 322223, 322232, 322233, 322322

Offset: 0

Roger L. Bagula, Apr 28 2010

Or: add two times the repunit of matching length to A007088(n).

			0+2, 1+2, 10+22, 11+22, 100+222, 101+222, 110+222, 111+222, 1000+2222, 1001+2222,...

Table[Sum[Table[((Reverse[IntegerDigits[n, 2]]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]][[m]]*10^( m - 1), {m, 1, Length[Table[((Reverse[IntegerDigits[n, 2]]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]]]}], {n, 1, 51}]
Table[FromDigits[2 + IntegerDigits[n, 2]], {n, 0, 100}]

a(n) = A007088(n)+A002276(A070939(n)).

A361820 Palindromes in A329150.

Original entry on oeis.org

0, 2, 3, 5, 7, 11, 22, 33, 55, 77, 202, 222, 232, 252, 272, 303, 313, 323, 333, 353, 373, 505, 525, 535, 555, 575, 707, 717, 727, 737, 757, 777, 1111, 2002, 2112, 2222, 2332, 2552, 2772, 3003, 3113, 3223, 3333, 3553, 3773, 5005, 5115, 5225, 5335, 5555, 5775, 7007, 7117

Offset: 1

Bernard Schott, Mar 25 2023

If m is a palindrome with no digit greater than 5 in A118597, then A329147(m) is a term, but there exist terms that are not of this form as 313, 717, ...

			232 is a term which has two preimages since A329147(91) = A329147(121) = 232.
313 = A329147(26) is a term whose preimage is not in A118597.
2002 is a term since A329147(1001) = 2002.
2112 is a term since A329147(151) = 2112.
27172 = A329147(1471) is a term whose preimage is not in A118597.

Intersection of A002113 and A329150.
Cf. A118597, A329147, A361750, A361821.
Subsequences: A002276, A002277, A002279, A002281, A099814.

p[n_] := If[n > 0, Prime[n], 0]; seq[ndigmax_] := Module[{t = Table[FromDigits[ Flatten@ IntegerDigits@ (p /@ IntegerDigits[n])], {n, 0, 10^ndigmax - 1}]}, Union@ Select[t, # < 10^ndigmax && PalindromeQ[#] &]]; seq[4] (* Amiram Eldar, Mar 26 2023 *)

ispal(n) = my(d=digits(n)); d==Vecrev(d);
f(n) = if (n, fromdigits(concat(apply(d -> if (d, digits(prime(d)), [0]), digits(n)))), 0); \\ A329147
lista(nn) = my(list = List(), m); for (n=0, nn, m = f(n); if ((m <= nn) && ispal(m), listput(list, m));); vecsort(Set(list)); \\ Michel Marcus, Mar 26 2023

A380435 Erase digit 0 from decimal expansion of n. Then repeatedly apply the number of divisor function (A000005) onto each digit until a stationary value is reached. a(n) is the final stationary value (if it is reached for all digits).

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 11, 12, 12, 12, 12, 12, 12, 12, 12, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22

Offset: 1

Ctibor O. Zizka, Jan 24 2025

The number of iterations is 0, 1, 2, 3 for numbers containing the highest digits (1, 2), (3,5,7), (4, 9), (6, 8). n >= a(n) >= 1.

			For n = 21 a(21) = 21.
For n = 408 we iterate 48 --> 34 --> 23 --> 22, thus, after 3 iterations, a(408) = 22.

Cf. A002275, A002276 - A002283, A004719, A007931, A111066.

a[n_] := FromDigits[IntegerDigits[n] /. {0 -> Nothing, ?(# > 1 &) -> 2}]; Array[a, 100] (* _Amiram Eldar, Jan 24 2025 *)

a(A007931(n)) = A007931(n).
For r = 1, k >= 0:
a(10^k) = 1
a((10^k - 1)/9) = (10^k - 1)/9.
For r from [2, 9], k >= 0:
a(r*10^k) = 2.
a(r*(10^k - 1)/9) = 2*(10^k - 1)/9.

cp's OEIS Frontend

A176894 Increase each digit in the binary representation of n by 2.

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A361820 Palindromes in A329150.

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A380435 Erase digit 0 from decimal expansion of n. Then repeatedly apply the number of divisor function (A000005) onto each digit until a stationary value is reached. a(n) is the final stationary value (if it is reached for all digits).

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