A060418 -id:A060418 - cp's OEIS frontend

A262401 In prime factorization of n: replace each factor with its largest decimal digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 3, 14, 15, 16, 7, 18, 9, 20, 21, 2, 3, 24, 25, 6, 27, 28, 9, 30, 3, 32, 3, 14, 35, 36, 7, 18, 9, 40, 4, 42, 4, 4, 45, 6, 7, 48, 49, 50, 21, 12, 5, 54, 5, 56, 27, 18, 9, 60, 6, 6, 63, 64, 15, 6, 7, 28, 9, 70, 7, 72, 7, 14

Offset: 1

Reinhard Zumkeller, Sep 25 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A054055, A027746, A001222, A002473, A006530, A060418, A068191.

a262401 = product . map a054055 . a027746_row'

Array[Times @@ (Power[Max@ IntegerDigits[#1], #2] & @@@ FactorInteger[#]) &, 74] (* Michael De Vlieger, Jan 23 2022 *)

a(n) = my(f=factor(n)); for (k=1, #f~, f[k,1] = vecmax(digits(f[k,1]))); factorback(f); \\ Michel Marcus, Jan 22 2022

Multiplicative with p -> A054055(p), p prime.
a(n) = Product_{k=1..A001222(n)} A054055(A027746(n,k)).
a(n) <= n.
a(m) = m iff m is 7-smooth:
  a(A002473(n)) = A002473(n) and a(A068191(n)) < A068191(n).
A006530(a(n)) <= 7.
a(a(n)) = a(n).

A090194 Primes which when multiplied by their largest digit and 1 is added form another prime.

Original entry on oeis.org

2, 43, 61, 263, 433, 461, 601, 641, 653, 661, 821, 857, 1061, 1063, 1187, 1361, 1423, 1487, 1613, 1811, 1871, 1877, 2063, 2081, 2143, 2161, 2621, 2801, 2837, 3061, 3163, 3581, 3623, 3631, 3643, 3851, 4561, 5087, 5261, 5381, 5623, 5807, 5861, 6011, 6053

Offset: 1

Enoch Haga, Jan 22 2004

			a(2)=43. Largest digit is 4. Multiply 43*4=172. 172+1=173, prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A060418.

Select[Prime[Range[1000]],PrimeQ[1+#*Max[IntegerDigits[#]]]&] (* Harvey P. Dale, May 21 2024 *)

isok(p) = isprime(p) && isprime(p*vecmax(digits(p))+1); \\ Michel Marcus, Jun 08 2014

In the prime sequence, select largest digit in each prime, multiply by the prime containing that digit, then add 1. If the result is another prime, add to sequence.

A090195 Primes which when multiplied by their largest digit and 1 is subtracted form another prime.

Original entry on oeis.org

2, 41, 163, 181, 211, 431, 463, 613, 653, 853, 1163, 1381, 1483, 1613, 1801, 1861, 1873, 2011, 2063, 2141, 2221, 2243, 2411, 2633, 2851, 3041, 3181, 3583, 3623, 4211, 4241, 4363, 4421, 4463, 4483, 4603, 5563, 5581, 5821, 5851, 6113, 6143, 6203, 6553

Offset: 1

Enoch Haga, Jan 22 2004

			a(2)=41. Largest digit is 4. Multiply 41*4=164. 164-1=163, prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A060418.

Select[Prime[Range[1000]],PrimeQ[# Max[IntegerDigits[#]]-1]&] (* Harvey P. Dale, Dec 31 2019 *)

isok(p) = isprime(p) && isprime(p*vecmax(digits(p))-1); \\ Michel Marcus, Jun 08 2014

In the prime sequence, select largest digit in each prime, multiply by the prime containing that digit, then subtract 1. If the result is another prime, add to sequence.

A155476 Primes p such that p and the p-th prime have the same largest digit.

Original entry on oeis.org

7, 29, 37, 73, 97, 109, 137, 139, 149, 181, 239, 271, 281, 283, 293, 307, 367, 379, 397, 419, 449, 499, 557, 577, 593, 599, 631, 659, 691, 733, 751, 839, 877, 881, 883, 911, 919, 971, 977, 1109, 1129, 1193, 1229, 1249, 1283, 1289, 1291, 1307, 1429, 1489

Offset: 1

Juri-Stepan Gerasimov, Jan 23 2009

			7 (prime) is a term because prime(7)=17 and 7 and 17 have 7 as their largest digit.
29 (prime) is a term because prime(29)=109 and 29 and 109 have 9 as their largest digit.
37 (prime) is a term because prime(37)=157 and 37 and 157 have 7 as their largest digit.

Jinyuan Wang, Table of n, a(n) for n = 1..10000

Cf. A000040 (primes), A054055, A060418.

A054055 := proc(n) max( op(convert(n,base,10)) ) ; end proc:
for n from 2 to 2200 do if isprime(n) then if A054055(n) = A054055(ithprime(n)) then printf("%d,",n) ; end if; end if; end do: # R. J. Mathar, May 10 2010

forprime(p=1,1489,if(vecmax(digits(p))==vecmax(digits(prime(p))),print1(p,", "))) \\ Jinyuan Wang, Feb 13 2019

Most terms > 300 corrected by R. J. Mathar, May 10 2010

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A262401 In prime factorization of n: replace each factor with its largest decimal digit.

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A090194 Primes which when multiplied by their largest digit and 1 is added form another prime.

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A090195 Primes which when multiplied by their largest digit and 1 is subtracted form another prime.

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A155476 Primes p such that p and the p-th prime have the same largest digit.

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