A202266 -id:A202266 - cp's OEIS frontend

A202265 Nonprime numbers in which all substrings and reversal substrings are nonprimes.

0, 1, 4, 6, 8, 9, 10, 18, 40, 44, 46, 48, 49, 60, 64, 66, 68, 69, 80, 81, 84, 86, 88, 90, 94, 96, 99, 100, 108, 180, 184, 186, 400, 404, 406, 408, 440, 444, 446, 448, 460, 464, 466, 468, 469, 480, 481, 484, 486, 488, 490, 494, 496, 600, 604, 606, 608, 609

Offset: 1

Jaroslav Krizek, Dec 25 2011

Subsequence of A062115, A202259.

Supersequence of A202266.

			All substrings and reversal substrings of 186 are nonprimes: 1, 6, 8, 18, 68, 81, 86, 186, 681.

Harvey P. Dale, Table of n, a(n) for n = 1..2000

Cf. A202263 (primes in which all substrings and reversal substrings are primes), A068669 (noncomposite numbers in which all substrings and reversal substrings are noncomposites), A202266 (composite numbers in which all substrings and reversal substrings are composites).

Select[Range[0,1000],NoneTrue[Union[Flatten[{#,IntegerReverse[#]}&/@Flatten[Table[ FromDigits/@Partition[IntegerDigits[#],d,1],{d,IntegerLength[#]}]]]],PrimeQ]&] (* Harvey P. Dale, Jul 30 2024 *)

Corrected (498 deleted) by Harvey P. Dale, Jul 30 2024

A202263 Primes in which all substrings and reversal substrings are primes.

Original entry on oeis.org

2, 3, 5, 7, 37, 73, 373

Offset: 1

Jaroslav Krizek, Dec 25 2011

Sequence is finite with 7 terms.

Subsequence of A085823, A068669, A024770, A012883.

			All substrings and reversal substrings of 373 are primes:3, 7, 37, 73, 373.

Cf. A202264 (noncomposite numbers in which all substrings and reversal substrings are noncomposite), A202265 (nonprimes in which all substrings and reversal substrings are nonprimes), A202266 (composite numbers in which all substrings and reversal substrings are composites).

A202264 Noncomposite numbers in which all substrings and reversal substrings are noncomposites.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 113, 131, 311, 313, 373

Offset: 1

Jaroslav Krizek, Dec 25 2011

Sequence is finite with 17 terms.
Supersequence of A202263, A085823.
Subsequence of A068669, A012883, A024770, A012883.

			All substrings and reversal substrings of 311 are noncomposites: 1, 3, 11, 13, 31, 113, 311.

Cf. A202263 (primes in which all substrings and reversal substrings are primes), A202265 (nonprimes in which all substrings and reversal substrings are nonprimes), A202266 (composite numbers in which all substrings and reversal substrings are composites).

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A202265 Nonprime numbers in which all substrings and reversal substrings are nonprimes.

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A202263 Primes in which all substrings and reversal substrings are primes.

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A202264 Noncomposite numbers in which all substrings and reversal substrings are noncomposites.

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