A066737 -id:A066737 - cp's OEIS frontend

A167458 Indices of numbers in A167459 which are not in A066737.

24, 25, 26, 27, 53, 54, 55, 88, 89, 90, 124, 125, 126, 127, 181, 182, 183, 215, 216, 268, 269, 270, 271, 303, 304, 305, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364

Offset: 1

M. F. Hasler, Nov 19 2009

Also, indices of terms in A167459 which are in A166505 (or: which are not in A152242).

Cf. A166504, A152242.

c=0; for(n=1,9999, is_A167459(n) & c++ & !is_A152242(n) & print1(c", "))

A152242 Integers formed by concatenating primes.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 47, 52, 53, 55, 57, 59, 61, 67, 71, 72, 73, 75, 77, 79, 83, 89, 97, 101, 103, 107, 109, 112, 113, 115, 117, 127, 131, 132, 133, 135, 137, 139, 149, 151, 157, 163, 167, 172, 173, 175, 177, 179

Offset: 1

Eric Angelini, Oct 15 2009

Leading zeros are not allowed (cf. A166504).

For any k > 0, there are A246806(k) terms with k digits. - Rémy Sigrist, Jan 08 2023

			101 is a member since it is prime; 303 is not since it is composite and 30 is also not a prime.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Henri Picciotto, Selected Integer Sequences

Cf. A019549, A038692, A066737, A105184, A129800, A166504, A246806.

is_A152242(n)=/* If n is even, the last digit must be 2 and [n\10] (if nonzero) must be in this sequence. (This check is not necessary but improves speed.) */ bittest(n,0) || return( n%10==2 && (n<10 || is_A152242(n\10))); isprime(n) && return(1); for(i=1,#Str(n)-1, n%10^i>10^(i-1) && isprime( n%10^i ) && is_A152242( n\10^i) && return(1)) \\ M. F. Hasler, Oct 15 2009; edited Oct 16 2009, to disallow leading zeros

from sympy import isprime
def ok(n):
    if isprime(n): return True
    s = str(n)
    return any(s[i]!="0" and isprime(int(s[:i])) and ok(int(s[i:])) for i in range(1, len(s)))
print([k for k in range(180) if ok(k)]) # Michael S. Branicky, Sep 01 2024

More terms from M. F. Hasler and Zak Seidov, Oct 15 2009

A121609 Composite numbers that can be written as concatenation of two primes in decimal representation.

Original entry on oeis.org

22, 25, 27, 32, 33, 35, 52, 55, 57, 72, 75, 77, 112, 115, 117, 132, 133, 135, 172, 175, 177, 192, 195, 213, 217, 219, 231, 232, 235, 237, 243, 247, 253, 259, 261, 267, 273, 279, 289, 292, 295, 297, 312, 315, 319, 323, 329, 341, 343, 361, 371, 372, 375, 377

Offset: 1

Reinhard Zumkeller, Aug 10 2006

Subsequence of A066737.

			A002808(249) = 315 = 31*10+5 = A000040(11)*10+A000040(3),
therefore 315 is a term: a(44) = 315;
A002808(252) = 319 = 3*100+19 = A000040(2)*100+A000040(8),
therefore 319 is a term: a(45) = 319.

Jean-Marc Falcoz, Table of n, a(n) for n = 1..11140

Cf. A121610, A105184, A121608.

A167459 Composite numbers in A166504, i.e., whose decimal expansion can be split up into prime numbers, with leading zeros allowed.

Original entry on oeis.org

22, 25, 27, 32, 33, 35, 52, 55, 57, 72, 75, 77, 112, 115, 117, 132, 133, 135, 172, 175, 177, 192, 195, 202, 203, 205, 207, 213, 217, 219, 222, 225, 231, 232, 235, 237, 243, 247, 252, 253, 255, 259, 261, 267, 272, 273, 275, 279, 289, 292, 295, 297, 302, 303

Offset: 1

M. F. Hasler, Nov 19 2009

In contrast to A066737 (which is a subsequence of this one), we allow for leading zeros in the "prime" substrings; the two sequences differ from n=24 on, with a(24)=202 which is not in A066737.

Sequence A166505 gives the difference, A167459 \ A066737 = A166504 \ A152242. Sequence A167458 gives the indices of the terms not in A066737.

Cf. A002808, A066737, A121609, A166504, A167505.

is_A167459(n) = !isprime(n) & is_A166504(n)

A167459 = A002808 n A166504, where "n" means intersection.

A167459 \ A066737 = A166504 \ A152242.

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A167458 Indices of numbers in A167459 which are not in A066737.

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A152242 Integers formed by concatenating primes.

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A121609 Composite numbers that can be written as concatenation of two primes in decimal representation.

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A167459 Composite numbers in A166504, i.e., whose decimal expansion can be split up into prime numbers, with leading zeros allowed.

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